Abrasive particles and methods of forming same

ABSTRACT

An abrasive particle having a body including a first major surface, a second major surface opposite the first major surface, and a side surface extending between the first major surface and the second major surface, such that a majority of the side surface comprises a plurality of microridges.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of and claims priority to U.S.Non-Provisional patent application Ser. No. 15/591,929, entitled“ABRASIVE PARTICLES AND METHODS OF FORMING SAME,” by Jennifer H.CZEREPINSKI et al., filed on May 10, 2017, which claims priority under35 U.S.C. § 119(e) to U.S. Provisional Patent Application No.62/334,298, entitled “ABRASIVE PARTICLES AND METHOD OF FORMING SAME,” byJennifer H. CZEREPINSKI et al., filed May 10, 2016, which are assignedto the current assignee hereof and incorporated herein by reference intheir entireties.

BACKGROUND Field of the Disclosure

The following is directed to abrasive particles, and more particularly,to abrasive particles having certain features and methods of formingsuch abrasive particles.

Description of the Related Art

Abrasive articles incorporating abrasive particles are useful forvarious material removal operations including grinding, finishing,polishing, and the like. Depending upon the type of abrasive material,such abrasive particles can be useful in shaping or grinding variousmaterials in the manufacturing of goods. Certain types of abrasiveparticles have been formulated to date that have particular geometries,such as triangular abrasive particles and abrasive articlesincorporating such objects. See, for example, U.S. Pat. Nos. 5,201,916;5,366,523; and 5,984,988.

Previously, three basic technologies that have been employed to produceabrasive particles having a specified shape, which are fusion,sintering, and chemical ceramic. In the fusion process, abrasiveparticles can be shaped by a chill roll, the face of which may or maynot be engraved, a mold into which molten material is poured, or a heatsink material immersed in an aluminum oxide melt. See, for example, U.S.Pat. No. 3,377,660. In sintering processes, abrasive particles can beformed from refractory powders having a particle size of up to 10micrometers in diameter. Binders can be added to the powders along witha lubricant and a suitable solvent to form a mixture that can be shapedinto platelets or rods of various lengths and diameters. See, forexample, U.S. Pat. No. 3,079,242. Chemical ceramic technology involvesconverting a colloidal dispersion or hydrosol (sometimes called a sol)to a gel or any other physical state that restrains the mobility of thecomponents, drying, and firing to obtain a ceramic material. See, forexample, U.S. Pat. Nos. 4,744,802 and 4,848,041. Other relevantdisclosures on abrasive particles and associated methods of forming andabrasive articles incorporating such particles are available at:http://www.abel-ip.com/publications/.

The industry continues to demand improved abrasive materials andabrasive articles.

SUMMARY

According to one aspect, an abrasive particle includes a body includinga first major surface, a second major surface opposite the first majorsurface, and a side surface extending between the first major surfaceand the second major surface, wherein the side surface comprises a MeanAnisotropy Factor of at least 1.25.

According to another aspect, an abrasive particle includes a bodyincluding a first major surface, a second major surface opposite thefirst major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein the first majorsurface comprises a first protrusion disposed abutting the first sidesurface portion and extending along at least a portion of the first sidesurface portion, and further comprising an untextured region extendingthrough a central region of the body, wherein the untextured regiondefines a majority of a total surface area of the first major surface.

In yet another aspect, an abrasive particle includes a body including afirst major surface, a second major surface opposite the first majorsurface, and a side surface extending between the first major surfaceand the second major surface, wherein a majority of the side surfacecomprises a plurality of microridges.

According to yet another aspect, a collection of abrasive particlesincludes a first abrasive particle comprising a body including a firstmajor surface, a second major surface opposite the first major surface,and a side surface extending between the first major surface and thesecond major surface, wherein the body of the first abrasive particlecomprises a first two-dimensional shape, and wherein the first majorsurface comprises a first protrusion abutting and extending along atleast a portion of a first side surface portion of the side surface, andwherein the body further comprises an untextured region extendingthrough a central region of the body, wherein the untextured regiondefines a majority of a total surface area of the first major surface,and further including a second abrasive particle comprising a bodyincluding a first major surface, a second major surface opposite thefirst major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein the body of thesecond abrasive particle comprises a two-dimensional shape that isdifferent compared to the two-dimensional shape of the first abrasiveparticle.

In yet another aspect, a collection of abrasive particles comprisesabrasive particles, wherein each particle of the collection of abrasiveparticles includes a body having a first major surface, a second majorsurface opposite the first major surface, and a side surface extendingbetween the first major surface and the second major surface; andwherein a majority of the particles of the collection of abrasiveparticles comprises a plurality of microridges extending along at leasta portion of the sides surface.

According to still another aspect, a collection of abrasive particlescomprises abrasive particles, wherein a particle of the collection ofabrasive particles includes a body having a first major surface, asecond major surface opposite the first major surface, and a sidesurface extending between the first major surface and the second majorsurface, and wherein the side surface includes a plurality of sidesurface portions extending between external corners of the body andwherein at least 45% of the side surface portions of the body include aplurality of microridges.

One aspect includes a collection of abrasive particles, wherein eachabrasive particle of the collection of abrasive particles including abody having a first major surface, a second major surface opposite thefirst major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein the first majorsurface and second major surface are substantially parallel with eachother; and wherein the collection of abrasive particles comprises a MeanNon-Convexity Factor of at least 3.5 and a Non-Convexity Factor StandardDeviation of at least 2.4.

Another aspect includes a collection of abrasive particles, wherein eachabrasive particle of the collection of abrasive particles comprises abody having a first major surface, a second major surface opposite thefirst major surface, and a side surface extending between the firstmajor surface and the second major surface, and wherein the collectionof abrasive particles comprises a Mean Anisotropy Factor of at least1.25.

And yet another aspect includes a collection of abrasive particles,wherein each abrasive particle of the collection of abrasive particlescomprises a body having a first major surface, a second major surfaceopposite the first major surface, and a side surface extending betweenthe first major surface and the second major surface, wherein the bodycomprises a height as defined as the distance along the side surfacebetween the first major surface and the second major surface wherein thecollection of abrasive particles comprises a standard deviation ofheight of not greater than 100 microns, and wherein the collection ofabrasive particles comprises a Mean Non-Convexity Factor of at least3.5.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure may be better understood, and its numerousfeatures and advantages made apparent to those skilled in the art byreferencing the accompanying drawings.

FIG. 1 includes a schematic of a method of forming an abrasive particlein accordance with an embodiment.

FIG. 2A includes a top-down view of the system for forming an abrasiveparticle according to an embodiment.

FIG. 2B includes a cross-sectional view of a portion of the bodyincluding features according to an embodiment.

FIGS. 3A, 3B, and 4A-4L include top-down and perspective viewillustrations of forms used to modify a body according to embodiments.

FIG. 5 includes a perspective view illustration of a shaped abrasiveparticle.

FIG. 6 includes a perspective view illustration of a randomly shapedabrasive particle.

FIG. 7A includes a perspective view illustration of a controlled heightabrasive particle according to an embodiment.

FIG. 7B includes a perspective view illustration of a controlled heightabrasive particle according to an embodiment.

FIG. 7C includes a top-down view illustration of an abrasive particleaccording to an embodiment.

FIG. 7D includes a side view illustration of a portion of a coatedabrasive according to an embodiment.

FIG. 8A includes an image of an abrasive particle according to anembodiment.

FIG. 8B includes top-down image of an abrasive particle according to anembodiment.

FIG. 8C includes a surface profile plot for a portion of the majorsurface of the abrasive particle of FIG. 8B.

FIG. 8D includes a surface profile plot for a portion of the majorsurface of the particle of FIG. 8B.

FIGS. 9A-9E include images of abrasive particles according toembodiments herein.

FIG. 10 includes a cross-sectional illustration of a coated abrasivearticle according to an embodiment.

FIG. 11 includes a cross-sectional illustration of a bonded abrasivearticle according to an embodiment.

FIGS. 12A-12J include top-down images of abrasive particles from acollection of abrasive particles according to an embodiment.

FIGS. 13A-13R include top-down images of abrasive particles from acollection of abrasive particles according to an embodiment.

FIGS. 14A-14J include top-down images of abrasive particles from acollection of abrasive particles according to an embodiment.

FIG. 15A includes an image of an abrasive particle including a pluralityof microridges on a side surface according to an embodiment.

FIG. 15B includes an image of the side surface of the abrasive particleof FIG. 15A according to an embodiment.

FIG. 16 includes an image of a portion of a side surface of an abrasiveparticle including scaled microridges according to an embodiment.

FIG. 17 includes an image of a portion of a side surface of an abrasiveparticle including expanding microridges according to an embodiment.

FIG. 18 includes a side view scanning electron microscope (SEM) image ofan abrasive particle according to an embodiment.

FIG. 19 includes a magnified SEM image of the side wall of the abrasiveparticle of FIG. 18.

FIG. 20 includes the side view image of FIG. 18 marked for measurementof the height of the body and the second region.

FIG. 21A includes a scanning electron microscope (SEM) image of aportion of a sidewall.

FIG. 21B includes the image of the FIG. 21A as analyzed using theFourier Transform.

FIG. 22A includes a top-down X-ray microscopy (XRM) image of an abrasiveparticle according to an embodiment.

FIG. 22B includes a binary image of FIG. 22A.

FIG. 22C includes a converted image of FIG. 22B using a convex hullanalysis via imaging processing software.

FIG. 23A includes a top-down XRM image of an abrasive particle fromSample CS1.

FIG. 23B includes a SEM image of a portion of a side surface of anabrasive particle from Sample CS1.

FIG. 24A includes a top-down image of an abrasive particle from SampleCS2.

FIG. 24B includes a SEM image of a portion of a side surface of anabrasive particle from Sample CS2.

FIG. 25A includes a top-down SEM image of an abrasive particle fromSample CS3.

FIG. 25B includes a SEM image of a portion of a side surface of anabrasive particle from Sample CS1.

DETAILED DESCRIPTION

The following is directed to methods of forming abrasive particles andfeatures of such abrasive particles. The abrasive particles may be usedin various abrasive articles, including for example bonded abrasivearticles, coated abrasive articles, and the like. Alternatively, theabrasive particles of the embodiments herein may be utilized in freeabrasive technologies, including for example grinding and/or polishingslurries.

FIG. 1 includes an illustration of a system for forming an abrasiveparticle in accordance with an embodiment. The process of forming theabrasive particles can be initiated by forming a mixture 101 including aceramic material and a liquid. In particular, the mixture 101 can be agel formed of a ceramic powder material and a liquid, wherein the gelcan be characterized as a shape-stable material having the ability tohold a given shape even in the green (i.e., unfired) state. Inaccordance with an embodiment, the gel can include a powder materialthat is an integrated network of discrete particles.

The mixture 101 can be formed to have a particular content of solidmaterial, such as the ceramic powder material. For example, in oneembodiment, the mixture 101 can have a solids content within a range ofat least 25 wt % and not greater than 75 wt % for the total weight ofthe mixture 101.

According to one embodiment, the ceramic powder material can include anoxide, a nitride, a carbide, a boride, an oxycarbide, an oxynitride, anda combination thereof. In particular instances, the ceramic material caninclude alumina. More specifically, the ceramic material may include aboehmite material, which may be a precursor of alpha alumina. The term“boehmite” is generally used herein to denote alumina hydrates includingmineral boehmite, typically being Al2O3•H2O and having a water contenton the order of 15%, as well as pseudoboehmite, having a water contenthigher than 15%, such as 20-38% by weight. It is noted that boehmite(including pseudoboehmite) has a particular and identifiable crystalstructure, and accordingly unique X-ray diffraction pattern, and assuch, is distinguished from other aluminous materials including otherhydrated aluminas such as ATH (aluminum trihydroxide) a common precursormaterial used herein for the fabrication of boehmite particulatematerials.

Furthermore, the mixture 101 can be formed to have a particular contentof liquid material. Some suitable liquids may include organic materials.Other suitable materials can include water. In accordance with oneembodiment, the mixture 101 can be formed to have a liquid content lessthan the solids content of the mixture 101. In more particularinstances, the mixture 101 can have a liquid content within a range ofat least about 25 wt % and not greater than 75 wt % for the total weightof the mixture 101. The water content of the mixture 101 may becontrolled to facilitate suitable drying upon shrinkage, which mayassist with the formation of abrasive particles according to theembodiments herein.

Furthermore, to facilitate processing and forming abrasive particlesaccording to embodiments herein, the mixture 101 can have a particularstorage modulus. For example, the mixture 101 can have a storage moduluswithin a range of at least about 1×10⁴ Pa and not greater than about1×10⁷ Pa. The storage modulus can be measured via a parallel platesystem using ARES or AR-G2 rotational rheometers, with Peltier platetemperature control systems. For testing, the mixture 101 can beextruded within a gap between two plates that are set to beapproximately 8 mm apart from each other. After extruding the gel intothe gap, the distance between the two plates defining the gap is reducedto 2 mm until the mixture 101 completely fills the gap between theplates. After wiping away excess mixture, the gap is decreased by 0.1 mmand the test is initiated. The test is an oscillation strain sweep testconducted with instrument settings of a strain range between 0.1% to100%, at 6.28 rad·s⁻¹ (1 Hz), using 25-mm parallel plate and recording10 points per decade. Within 1 hour after the test completes, the gap islowered again by 0.1 mm and the test is repeated. The test can berepeated at least 6 times. The first test may differ from the second andthird tests. Only the results from the second and third tests for eachspecimen should be reported. The viscosity can be calculated by dividingthe storage modulus value by 6.28 s⁻¹.

Furthermore, to facilitate processing and forming abrasive particlesaccording to embodiments herein, the mixture 101 can have a particularviscosity, which may facilitate later processing (e.g., modification)and formation of the desired abrasive particles. For example, themixture 101 can have a viscosity of at least about 4×10³ Pa·s, at leastabout 5×10³ Pa·s, at least about 6×10³ Pa·s, at least about 8×10³ Pa·s,at least about 10×10³ Pa·s, at least about 20×10³ Pa·s, at least about30×10³ Pa·s, at least about 40×10³ Pa·s, at least about 50×10³ Pa·s, atleast about 60×10³ Pa·s, or even at least about 65×10³ Pa·s. In at leastone non-limiting embodiment, the mixture 101 may have a viscosity of notgreater than about 1×10⁶ Pa·s, not greater than about 5×10⁵ Pa·s, notgreater than about 3×10⁵ Pa·s, or even not greater than about 2×10⁵Pa·s. It will be appreciated that the viscosity of the mixture 101 canbe within a range between any of the minimum and maximum values notedabove.

Moreover, the mixture 101 can be formed to have a particular content oforganic materials, including for example, organic additives that can bedistinct from the liquid, to facilitate processing and formation ofabrasive particles according to the embodiments herein. Some suitableorganic additives can include stabilizers, plasticizers, surfactants,binders, such as fructose, sucrose, lactose, glucose, UV curable resins,and the like.

The embodiments herein may utilize a mixture 101 having a particularcontent of organic additives. For example, the content of organicmaterials within the mixture 101, particularly, any of the organicadditives noted above may be a minor amount as compared to othercomponents within the mixture 101. In at least one embodiment, themixture 101 can have not greater than about 30 wt % organic material forthe total weight of the mixture 101. In other instances, the amount oforganic materials may be less, such as not greater than about 15 wt %,not greater than about 10 wt %, or even not greater than about 5 wt %.Still, in at least one non-limiting embodiment, the amount of organicmaterials within the mixture 101 can be at least about 0.1 wt %, such asat least about 0.5 wt % for the total weight of the mixture 101. It willbe appreciated that the amount of organic materials in the mixture 101can be within a range between any of the minimum and maximum valuesnoted above.

Moreover, the mixture 101 can be formed to have a particular content ofacid and/or base to facilitate processing and formation of abrasiveparticles according to the embodiments herein. Some suitable acids orbases can include nitric acid, sulfuric acid, citric acid, chloric acid,tartaric acid, phosphoric acid, ammonium nitrate, ammonium citrate.According to one particular embodiment, the mixture 101 can have a pH ofless than about 5, and more particularly, within a range between about 2and about 4, using a nitric acid additive.

The process of forming the abrasive particles can include forming themixture 101 into a body. Referencing FIG. 1, the system 100 can includea die 103 and define a deposition zone wherein the mixture 101 is formedinto the body 111. As illustrated, the mixture 101 can be providedwithin the interior of the die 103 and configured to be extruded througha die opening 105 positioned at one end of the die 103. As furtherillustrated, forming can include applying a force 180 (that may betranslated into a pressure) on the mixture 101 to facilitate moving themixture 101 through the die opening 105. In accordance with anembodiment, a particular pressure may be utilized during extrusion. Forexample, the pressure can be at least about 10 kPa, such as at leastabout 500 kPa. Still, in at least one non-limiting embodiment, thepressure utilized during extrusion can be not greater than about 10 MPaor not greater than 5 MPa. It will be appreciated that the pressure usedto extrude the mixture 101 can be within a range between any of theminimum and maximum values noted above.

In certain systems, the die 103 can include a die opening 105 having aparticular shape. It will be appreciated that the die opening 105 may beshaped to impart a particular shape to the mixture 101 and the resultingbody 111. Furthermore, the mixture 101 extruded through the die opening105 and the resulting body 111 can have essentially the samecross-sectional shape as the die opening 105. In accordance with anembodiment, the die opening 105 can have a rectangular shape. In stillother embodiments, the die opening 105 can be shaped to create certainfeatures in one or more surfaces of the body 111 as the mixture exitsthe die 103. The features can include a controlled distribution offeatures. Thus in certain instances, extrusion of the mixture 101 fromthe die 103 and modification of the body 111 can happen simultaneously.That is, the mixture 101 can exit the die 103 and be formed into a body111 having certain features in one or more surfaces, such that theduring forming of the body 111, the body 111 is also modified to includeone or more features in one or more surfaces of the body 111.

As further illustrated in FIG. 1, the mixture 101 may be extruded onto asubstrate. In the illustrated embodiment of FIG. 1, the substrate is inthe form of a belt 109 underlying the die 103, such that the resultingbody 111 is in the form or a layer or sheet of material. Other types ofsubstrates may be utilized. In specific instances, the mixture 101 canbe extruded directly onto the belt 109, which may facilitate continuousprocessing.

According to one particular embodiment, the belt 109 can be formed tohave a film overlying a substrate, wherein the film can be a discreteand separate layer of material configured to facilitate processing andforming of abrasive particles. The process can include providing themixture 101 directly onto the film of the belt to form the body 111. Incertain instances, the film can include a polymer material, such aspolyester. In at least one particular embodiment, the film can consistessentially of polyester.

In still another embodiment, the upper surface of the belt 109 can havea particular roughness, which may facilitate formation of the abrasiveparticles according to the embodiments herein. For example, theroughness of the surface of the belt 109 may impact the manner in whichthe body 111 is dried and may facilitate controlled cracking of the body111. Various materials can be used for the belt 109 or as a coating onthe surface of the belt 109. Some suitable materials can includeinorganic materials, such as metal, metal alloys, ceramics,polycrystalline materials, amorphous phase materials, monocrystallinematerials, or any combination thereof. In another embodiment, the belt109 or upper surface of the belt 109 can include an organic material,such as a polymer, which may include materials such as epoxies, resins,thermosets, thermoplastics, polyimides, polyamides, and a combinationthereof. It will be appreciated that the upper surface of the belt 109may include one or more features, which are described in embodimentsherein, which may be used to form a distribution of features in aportion of the body 111, such as the portion of the body 111 in contactwith the upper surface of the belt 109 having such features. Forexample, aspects of the belt 109, such as surface roughness, material ofthe belt and the like, may be tailored to the specific aspects of thebody 111 and the forming process to facilitate suitable formation ofabrasive particles as described in embodiment herein.

In some embodiments, the belt 109 can be translated while moving themixture 101 through the die opening 105. As illustrated in the system100, the mixture 101 may be extruded in a direction 191. The directionof translation 110 of the belt 109 can be angled relative to thedirection of extrusion 191 of the mixture. While the angle between thedirection of translation 110 and the direction of extrusion 191 areillustrated as substantially orthogonal in the system 100, other anglesare contemplated, including for example, an acute angle or an obtuseangle. Moreover, while the mixture 101 is illustrated as being extrudedin a direction 191, which is angled relative to the direction oftranslation 110 of the belt 109, in an alternative embodiment, the belt109 and mixture 101 may be extruded in substantially the same direction.

The belt 109 may be translated at a particular rate to facilitateprocessing. For certain processes according to embodiments herein, therate of translation of the belt 109 as compared to the rate of extrusionof the mixture 101 in the direction 191 may be controlled to facilitateproper processing. For example, the rate of translation of the belt 109can be essentially the same as the rate of extrusion to ensure formationof a suitable body 111.

For certain embodiments, the mixture 101 may be extruded to form a body111 in the form of a body 111 having a generally rectangularcross-sectional shape as viewed in a plane defined by a height and widthof the body 111. While the body 111 is illustrated as a sheet, it willbe appreciated that the process is not so limited and the mixture can beformed into a body having any desired shape.

The process of forming the body 111 from the mixture 101 can includecontrol of particular features and process parameters to facilitatesuitable formation of abrasive particles having one or more features asprovided in the embodiments herein. For example, in certain instances,the process of forming a body 111 from the mixture 101 can includeforming a body 111 having a particular height. Moreover, it is notedthat the height 181 of the body 111 can be controlled by varying adistance between the die 103 and the surface of the belt 109.Alternatively, the process may use a doctor blade or similar techniqueto control the height 181 of the body 111. Additionally, forming themixture 101 into the body 111 can include controlling the dimensions ofthe body 111 based in part upon the viscosity of the mixture 101. In atleast one embodiment, the body 111 is formed into a large layer ofmaterial having a first major surface having a major surface area of atleast 10 cm², such as at least 20 cm² or at least 50 cm² or at least 100cm² or at least 500 cm² or at least 1 m². Notably, the process offorming the body 111 may be conducted without the use of a mold or otherproduction tool to form a plurality of individual and discrete portionsof gel contained within openings of a production tool.

Furthermore, to facilitate processing and forming abrasive particlesaccording to embodiments herein, the body 111, can have a particularviscosity, which can have any of the values noted above for theviscosity of the mixture 101.

The body 111 can have particular dimensions, including for example, alength (l), a width (w), and a height (h). In accordance with anembodiment, the body 111 may have a length that extends in the directionof the translating belt 109, which can be greater than the width,wherein the width of the body 111 is a dimension extending in adirection perpendicular to the length of the belt 109 and to the lengthof the sheet. The body 111 can have a height 181, wherein the length andwidth are greater than the height 181 of the body 111. As such,according to one embodiment, the length>width>height.

Notably, the height 181 of the body 111 can be the dimension extendingvertically from the surface of the belt 109. In accordance with anembodiment, the body 111 can be formed to have a particular dimension ofheight 181, wherein the height may be an average height of the body 111derived from multiple measurements. For example, the height 181 of thebody 111 can be at least about 0.1 mm, such as at least about 0.5 mm. Inother instances, the height 181 of the body 111 can be greater, such asat least about 0.8 mm, at least about 1 mm, at least about 1.2 mm, atleast about 1.6 mm, or even at least about 2 mm. Still, in onenon-limiting embodiment, the height 181 of the body 111 may be notgreater than about 10 mm, not greater than about 5 mm, or even notgreater than about 2 mm. It will be appreciated that the body 111 mayhave an average height within a range between any of the minimum andmaximum values noted above.

After extruding the mixture 101 from the die 103, the body 111 may betranslated in a direction 112 along the surface of the belt 109.Translation of the body 111 along the belt 109 may facilitate furtherprocessing. For example, after forming the body 111, the body 111 may betranslated to a modification zone 120, wherein at least a portion of thebody 111 is modified. The process of modifying the body 111 can includeusing one or more processes that can facilitate changing the stressgeneration within the body 111 during further processing. For example,the process of modifying the body 111 can include modifying portions ofthe body 111, such that upon further processing (e.g., drying), theportions of the body 111 associated with the modification can be regionsof higher stress concentrations compared to those regions that are notmodified, such that fracturing of the body may be more likely in theregions of higher stress concentrations, thus facilitating formingshaped precursor particles. For example, the process of modifying thebody 111 may locally alter the stress generation in the body 111 duringdrying. In one embodiment, the process of modifying can includedeforming at least a portion of the body 111. Modification of the body111 may facilitate the formation of at least one crack initiation pointin the body 111, such that during later processing (e.g., drying), theinitial position of a crack or defect and the direction of crackpropagation within the body 111 can be controlled. In one embodiment,the process of modifying the body 111 can include changing a physicalfeature of the body 111, such as an alteration of one or more surfacesand/or dimensions of the body 111.

In yet another embodiment, modifying at least portion of the body 111can include changing a chemical composition of at least a portion of thebody 111. In certain instances, modifying the body 111 can includechanging a rheological property of the body 111. In certain instances,the process of modifying the body 111 can include applying or providingat least one additive to at least a portion of the body 111, such thatthe additive may chemically and/or physically alter the body 111. Theadditive may facilitate a change in the body that leads to regions ofhigher stress concentrations during further processing, which canfacilitate controlled fracturing of the body 111. Such modifications mayfacilitate changing the stress within the body 111, such that of thebody 111 includes regions of higher stress relative to other regionswithin the body 111 having a lower stress. The distribution of theregions of higher stress and lower stress may be controlled bycontrolling one or more parameters associated with the modificationprocess, including but not limited to, the control of the distributionof features formed in the body, control of the distribution of one ormore additives within the body, and the like. Notably, when the processof modifying the body 111 is combined with other processes (e.g.,certain drying conditions) it may facilitate formation of abrasiveparticles having the features described herein.

The process of modification and drying may have one or more parametersthat can be controlled and facilitate the formation of various types ofabrasive particles. For example, certain parameters that may influencethe characteristics of the finally-formed abrasive particles caninclude, but are not limited to, composition of the upper surface of thebelt 109, the surface roughness of the upper surface of the belt 109,the distribution of features formed in the body 111 during modification,the shape, size and/or cross-sectional shape of the distribution offeatures formed in the body 111 during modification, the distributionand type of one or more additives used during modification, therheological properties (e.g., viscosity, etc.) of the body 111, thesize, shape, and composition of raw materials within the body 111, theheight of the body 111, the depth of the features, drying temperature,relative humidity, drying rate, drying time, rate of translation throughthe drying environment, or any combination thereof.

In one particular embodiment, the process of modifying can includeforming a controlled distribution of features in at least a portion ofthe body. For example, as illustrated in FIG. 2A, which includes atop-down view of the system of FIG. 1, the upper surface 112 of the body111 can be deformed such that a series of depressions 121 can be formedin the upper surface 112. As illustrated in FIGS. 1 and 2A, thedepressions 121 can be in the form of lines extending along the width(w) and length of the body 111 and extending partially through theheight 181 of the body 111. It will be appreciated that while thedepressions 121 are illustrated as lines, other shapes and arrangementsof the depressions 121 can be used, depending upon the desired aspectsof the finally-formed abrasive particles. For example, the depressions121 can be formed to have various shapes or contours, such as curved,straight, dots, and a combination thereof.

According to one embodiment, the controlled distribution of features canbe defined as a pattern or array of features, having at least onerepeating unit. In another embodiment, the controlled distribution offeatures can be a random distribution of features, such that there is nodiscernable short-range or long-range order to the arrangement of thefeatures. Other examples of controlled distributions may include aradial pattern, a spiral pattern, a phyllotactic pattern, an asymmetricpattern, a self-avoiding random distribution, or any combinationthereof.

The features of the controlled distribution may include a variety ofshapes and/or structures. For example, the features may include at leastone of a protrusion, a depression, an interconnected structure, adiscrete and isolated structure, or any combination thereof. In at leastone embodiment, the features can have various cross-sectional shapes,including for example, but not limited to, a U-shape, a V-shape, and thelike. In certain instances, at least a portion of the body 111 can beformed to have a controlled distribution of features including aninterconnected network of depressions, such as illustrated in FIGS. 1and 2. In any of the embodiments, the features formed in the body 111can be the same in shape and size with respect to each other. Still, inanother embodiment, at least two features can be distinct from eachother based on shape, size, contour, cross-sectional shape, and thelike.

The size, shape and spacing of the features may be controlled andfacilitate formation of precursor abrasive particles, and thus thefinally-formed abrasive particles of a desired size. In one particularembodiment, the size, shape, and spacing between the features mayfacilitate formation of abrasive particles according to embodimentsherein. The desired spacing between the features may influence thetarget average particle size of the abrasive particles to be formed. Inat least one embodiment, the features may be formed to have sharpcorners or a small radius of curvature, which may effectivelyconcentrate the stress at the desired locations within the body 111 andfurther facilitate controlled cracking to generate the desired shape andsize of abrasive particles, which can include those abrasive particleshaving the features of the embodiments herein.

For at least one aspect, the size of the features in the body 111 can becontrolled to facilitate formation of abrasive particles according toembodiments herein. For example, the features can include at least onefeature having a length (Lf), a width (Wf) and a depth (Df). In at leastone embodiment, the length can be the longest dimension, the width canbe the second longest dimension in the same plane as the length, and thedepth can be the shortest dimension of the feature, which may be indirection perpendicular to the plane defined by the length and thewidth. Notably, in one embodiment Lf≥Wf≥Df. Still, in anotherembodiment, the body may have dimensions based on Lf≥Df≥Wf.

According to at least one embodiment, a feature may be in the form of adepression formed within the body 111. FIG. 2B includes across-sectional illustration of a portion of the body 111 after formingfeatures according to an embodiment. As illustrated, the features 121can include depressions 231 formed within and extending into the volumeof the body 111. The features 121 may also include protrusions 232formed within the body 111, and defining regions extending above theupper surface 121 of the body 111. Notably, the depressions 231 can havean average depth 194 (df) defined as the average distance between abottom surface 195 of the depression 231 and the upper surface 112 ofthe body 111. In at least one embodiment, the depressions 231 can beformed to have an average depth 194 that is at least 5% of the averageheight 181 of the body 111. In other instances, the average depth 194can be greater, such as at least 10% of the average height 181 of thebody 111 or at least 15% or at least 20% or at least 25% or at least 30%or at least 35% or at least 40% or at least 45% or at least 50% or atleast 55% or at least 60% or at least 65% or at least 70% or at least75% or at least 80% or at least 85% or at least 90% or at least 95%.Still, in one non-limiting embodiment, the average depth 194 can be notgreater than 99% of the average height 181 of the body 111, such as notgreater than 95% or not greater than 90% or not greater than 85% or notgreater than 80% or not greater than 75% or not greater than 70% or notgreater than 65% or not greater than 60% or not greater than 55% or notgreater than 50% or not greater than 45% or not greater than 40% or notgreater than 35% or not greater than 30% or not greater than 25% or notgreater than 20% or not greater than 15% or not greater than 10% or notgreater than 5%. Still, it will be appreciated that the average depth194 can be within a range including any of the minimum and maximumpercentages noted above. Control of the average depth 194 of thedepressions 231 may facilitate suitable processing and improvedformation of abrasive particles having the feature of the embodimentsherein. One or more of such features may be present within thefinally-formed abrasive particles.

In yet another embodiment, the protrusions 232 can define regions of thebody 111 extending above the upper surface 112 of the body 111. Theprotrusions 232 can have an average height 234 relative to the averageheight 181 of the body. For example, the protrusions 232 may have anaverage height that is at least 5% of the average height 181 of the body111. In other instances, the average height 234 of the protrusions 232can be greater, such as at least 10% of the average height 181 of thebody 111 or at least 15% or at least 20% or at least 25% or at least 30%or at least 35% or at least 40% or at least 45% or at least 50% or atleast 55% or at least 60% or at least 65% or at least 70% or at least75% or at least 80% or at least 85% or at least 90% or at least 95%.Still, in one non-limiting embodiment, the average height 234 can be notgreater than 99% of the average height 181 of the body 111, such as notgreater than 95% or not greater than 90% or not greater than 85% or notgreater than 80% or not greater than 75% or not greater than 70% or notgreater than 65% or not greater than 60% or not greater than 55% or notgreater than 50% or not greater than 45% or not greater than 40% or notgreater than 35% or not greater than 30% or not greater than 25% or notgreater than 20% or not greater than 15% or not greater than 10% or notgreater than 5%. It will be appreciated that the average height 234 canbe within a range including any of the minimum and maximum percentagesnoted above. Control of the average height 234 of the protrusions 232may facilitate suitable processing and improved formation of abrasiveparticles having the feature of the embodiments herein. One or more ofsuch features may be present within the finally-formed abrasiveparticles.

The protrusions 232 may result from the modification process. In certaininstances, when one or more depressions are formed the mixture of thebody 111 is moved, and the protrusions 232 may result in areas aroundthe depression 231. In other instances, the material of the body 111 mayadhere to the form used to modify the surface of the body 111, and whenthe form is being pulled away from the body 111 some material of thebody 111 may adhere to the form. Such adhesion between the form and thebody 111 may cause the formation of protrusions. In certain instances,it may be desirable to limit the formation of protrusions due toadhesion between the form and the body during the modification process.

According to one embodiment, the process of modifying the body 111 caninclude modifying at least one surface of the body 111. As illustratedin FIG. 1, the features 121 can be formed in the upper surface 112 ofthe body 111. Various mechanisms may be used to form the features 121 inone or more surfaces of the body 111. For example, as illustrated inFIG. 1, a form 122 having a shaped features 124 can be translated in adirection 123 such that the shaped features 124 contact the uppersurface 112 of the body 111 and deform the body 111 according to theshaped features 124. Some examples of such processes can include gravurerolling or embossing. Other suitable processes for deforming a surfaceof the body 111 may include pressing, punching, depositing, spraying,and the like.

In at least one embodiment, the features formed in at least a portion ofthe surface (e.g., the upper surface 112) of the body 111 can be createdby contacting a form to the surface of the body 111 to be modified. Theform can have one or more features (e.g., protrusions, walls, openings,etc.) that can be used to create corresponding features in the body 111.Referring briefly to FIG. 3, a top-down view illustration of a form isprovided. As illustrated, in at least one embodiment, the form 300 canbe a screen comprising portions 301 connected to each other and definingopenings 302 between the portions. The form 300 can be pressed into theupper surface 112 of the body 111 and deform the body 111 in the regionscontacted by the portions 301. Notably, the body 111 can be modified bythe form 300, such that at least a portion of the upper surface 112 ofthe body 111 can be deformed to have features corresponding to thefeatures of the form 300. In particular, the portions 301 can be pressedinto the body 111 to form depressions, which can be arranged relative toeach other in the same arrangement of the portions 301 of the form 300.Moreover, depending upon certain other processing parameters, theformation of the depressions 301 can simultaneously form protrusions, asthe material from the depressions is pushed aside and displaced, whichcan result in the formation of protrusions on the upper surface 112 ofthe body 111. FIG. 3B includes a perspective view illustration of theform of FIG. 3A.

It will be appreciated that various other forms may be used with theprocess. The forms can generally have any combination of features. Theshape, size, and arrangement of the features of the form may impact thesize and shape of the abrasive particles formed. Moreover, the featuresof the form may influence the shape features present in the abrasiveparticles. Such shape features are described in embodiments herein.Certain forms may utilize a particular arrangement of projections orwalls that are interconnected and define openings. FIGS. 3A, 3B, and4A-4F include forms having interconnected protrusions or walls to defineopenings. For example, FIG. 4A includes a top down view illustration ofa form according to an embodiment. FIG. 4B includes a perspective viewillustration of the form for FIG. 4A. The form of FIG. 4A includesportions 401 in the form of walls that are connected to each other anddefine openings 402 having a generally quadrilateral, and moreparticularly, rectangular two-dimensional shape as viewed top-down.

FIG. 4C includes a top-down view illustration of a form according to anembodiment. FIG. 4D includes a perspective view illustration of the formof FIG. 4C. The form of FIG. 4C includes portions 403 in the form ofwalls that are connected to each other and define openings 404 having agenerally irregular polygonal two-dimensional shape as viewed top-down.

FIG. 4E includes a top-down view illustration of a form according to anembodiment. FIG. 4F includes a perspective view illustration of the formof FIG. 4E. As illustrated, the form can have portions 431, which areconnected to each other and defining openings 432 between the portions431. The openings 432 can have a quadrilateral shape, and morespecifically a trapezoidal shape, and even more particularly, a righttrapezoidal shape, wherein the shape of the openings 432 include atleast two right angles (i.e., 90 degrees). It will be appreciated thatthe forms of the embodiments herein can include portions having anycombination of shape, size, arrangement, contour and the like. Theportions of the forms defining the openings can have a linear shape,arcuate shape, or any combination thereof. While the forms can includeprotrusions that are interconnected to define openings, other forms canbe used that do not necessarily include protrusions that areinterconnected. For example, the protrusions may include one or morediscrete and separate features that can be separated from adjacentprotrusions by gaps.

FIGS. 4G-4H include illustrations of forms having protrusions that arenot interconnected according to an embodiment.

FIG. 4G includes a top-down view illustration of another form accordingto an embodiment. FIG. 4H includes a perspective view illustration ofthe form of FIG. 4G. The form of FIG. 4G includes a plate 410 and aplurality of discrete projections or pins 411 extending from the plate410. The pins 411 are spaced apart from each other and can be arrangedin any distribution to create corresponding distribution of discrete andseparate depressions in at least a portion of the body 111. The pins 411are illustrated as having a generally conical shape. However, it will beappreciated that other shapes may be used, including for example, butnot limited to, cylindrical, frustoconical, pyramidal, frustopyramidal,and the like.

While the forms of the embodiments herein have been illustrated ashaving generally planar shapes, it will be appreciated that the form canhave various other shapes. For example, the forms can be in the shape ofa roller that is configured to roll over the body 111 and impartfeatures into the body 111. A form having such a shape may be suitablefor continuous processing operations.

FIG. 4I includes a top-down view illustration of a form according to anembodiment. FIG. 4J includes a perspective view illustration of the formof FIG. 4I. The form of FIG. 4I includes a plate 412 and a randomarrangement of protrusions 413 extending from the plate 412, which canbe used to create corresponding depressions in at least a portion of thesurface of the body prior to drying. The protrusions 413 have a randomshape and a random spacing relative to other protrusions 413 on theplate 412.

FIG. 4K includes a top-down view illustration of a form according to anembodiment. FIG. 4L includes a perspective view illustration of the formof FIG. 4K. The form of FIG. 4K includes a plate 414 and having a randomarrangement of protrusions 415 extending from the plate 414, which canbe used to create corresponding depressions in at least a portion of thesurface of the body prior to drying. The form of FIG. 4K includesdiscrete protrusions 415 have a generally elongated and linear shape.The protrusions 415 have a generally random spacing and orientationrelative to other protrusions 415 on the plate 414.

Moreover, as illustrated in FIGS. 4K and 4L, the upper surfaces of theprotrusions 415 can have an edge extending between two chamferedsurfaces. In other embodiments, the upper surface of the protrusions canbe generally flat, such as illustrated in the protrusions 431 of FIG.4E. It will be appreciated that the upper surfaces of the protrusionscan be given any suitable shape to facilitate suitable modification ofthe body and formation of the desired abrasive particles. The uppersurface may have a generally planar contour, an edge, a radiused orcurved profile, or any other shape.

Any of the forms of the embodiments herein can be made of a particularmaterial. For example, some suitable materials can include inorganicmaterials, organic materials, synthetic materials, natural materials, orany combination thereof. Some examples of inorganic materials caninclude metal, metal alloys, glass, ceramic, polycrystalline,monocrystalline, or any combination thereof. Some suitable organicmaterials can include polymers, such as epoxies, resins, thermosets,thermoplastics, polyimides, polyamides, or any combination thereof. Theform may be a composite material including any combination of materialsnoted herein. The material of the form, particularly of the protrusionsthat will be in contact with the body, may be made of a particularmaterial to limit the ability of the mixture to stick to the form. Incertain instances, the material of the form is selected to ensure thatthe material of the body (i.e., the mixture) will not adhere to thematerial of the form, such that the features formed in the surface ofthe body can be made efficiently, with the proper shape and resolution.A form that limits the adhesion between the body and the form may limitunintended distortions in the body during modification, and mayfacilitate improved control of the shape and size of the abrasiveparticles formed from the controlled cracking processes.

In at least one embodiment, the surface of the form may be coated with amaterial prior to contacting the form to the body. Such coatingmaterials may be permanent or temporary. The coating material can be aninorganic material, organic material, natural material, syntheticmaterial or any combination thereof. For example, in one particularembodiment, the coating material can be an oil, such as a lubricant.

In yet another embodiment, the surface of the form, and particularly theprotrusions to be contacting the portions of the body to cause themodification, may be coated with a chemical agent that will facilitateproper formation of the features in the body. The chemical agent may bea chemical element or chemical composition. The chemical agent may be anadditive that can assist with modification of the body as described inembodiments herein, including for example a dopant. The chemical agentmay be a permanent or temporary material added to the surface of theform. The chemical agent may be an inorganic material, organic material,natural material, synthetic material, or any combination thereof.

It will be appreciated that the features may be formed in othersurfaces. For example, in an alternative embodiment, a surface of thebelt 109 configured to contact the mixture 101 can be formed to havefeatures. Accordingly, during deposition of the mixture 101 onto thebelt 109, the body 111 can be formed and the features on the belt 109can impart features into the surface of the body 111 in contact with thefeature on the belt 109. As such, the process of forming the body andmodifying the body are conducted substantially simultaneously. Such analternative process may or may not be used with a separate modificationzone 120 wherein other surfaces of the body 111 may be modified asdescribed in the embodiments herein. For example, in one embodiment, theupper surface 112 of the body 111 and the lower surface of the body 111in contact with the belt 109 may be modified according to any of thetechniques described herein.

In at least one embodiment, the belt 109 can have an upper surfacehaving a particular surface roughness. The upper surface of the belt isconfigured to contact the mixture 101 and the body 111. The belt 109 maynot necessarily have any features, but may have a particular surfaceroughness that may facilitate later processing to form the abrasiveparticles. Notably, it has been observed that certain materials having acertain roughness may assist with drying and controlled cracking of thebody 111 to facilitate formation of the abrasive particles according toembodiments herein. In at least one embodiment, forming the mixture 101into the body 111 includes forming the mixture 101 on the belt, whereinthe belt has a controlled surface roughness and surface energy relativeto the mixture 101 to facilitate controlled cracking and formation of aplurality of precursor abrasive particles from the controlled crackingprocess.

As noted herein, in another embodiment, the processes of modifying thebody 111 can include providing one or more additives to at least aportion of the body 111. Such additives may be used to physically orchemically alter the body 111, such that during later processing (e.g.,drying) the additives may facilitate controlled cracking of the body toform precursor abrasive particles. The one or more additives can beapplied to one or more surfaces of the body 111, including for example,any of the exterior surfaces of body 111. Some suitable processes forapplying the one or more additives can include depositing, spraying,printing, blasting, scanning, ejecting, heating, and the like. The oneor more additives may be added as solid particles, a liquid, a gas or acombination thereof. The one or more additives may be added as part ofan additive composition, which may include the additives and othermaterials, such as a carrier fluid configured to contain the one or moreadditives for ease of processing and delivery of the additive to thebody 111.

Some suitable additives can include rheology modifiers, dopants, poreformers, volatilization agents, and the like. Examples of dopants caninclude, but is not limited to, alkali elements, alkaline earthelements, rare-earth elements, hafnium (Hf), zirconium (Zr), niobium(Nb), tantalum (Ta), molybdenum (Mo), and a combination thereof. Inparticular instances, the dopant can include an element such as lithium(Li), sodium (Na), potassium (K), magnesium (Mg), calcium (Ca),strontium (Sr), barium (Ba), scandium (Sc), yttrium (Y), lanthanum (La),cesium (Ce), praseodymium (Pr), niobium (Nb), hafnium (Hf), zirconium(Zr), tantalum (Ta), molybdenum (Mo), vanadium (V), chromium (Cr),cobalt (Co), iron (Fe), germanium (Ge), manganese (Mn), nickel (Ni),titanium (Ti), zinc (Zn), or any combination thereof. Some suitableexamples of rheology modifiers can include organic materials, acids,bases, or any combination thereof. Certain additives, such as thedopants, may be added during various phases of processing. For example,the dopants may be added during the formation of the mixture.Alternatively, the dopant may be added to the precursor abrasiveparticles after some drying and/or some calcination of the precursorabrasive particles.

It will also be appreciated that the mixture may include seed material,such as alpha alumina seeds or iron oxide seeds, which may assist withthe formation of a high temperature phase of material in thefinally-formed and sintered abrasive particles.

Some suitable examples of pore formers can include hollow particles madeof organic or inorganic materials, beads, spheres, glass, ceramics,glass-ceramics, natural materials, and the like. Some suitable inorganicmaterials can include oxides or carbon-containing materials, such asgraphite, salts such as such as sodium chloride, potassium chloride,magnesium chloride, calcium chloride, sodium silicate, sodium carbonate,sodium sulfate, potassium sulfate, magnesium sulfate, or any combinationthereof. In certain instances, the pore formers can include materialshaving low volatilization temperatures, such that upon furtherprocessing at suitable temperatures the pore formers volatilize forminga gas thereby leaving pores behind in the body 111. Some exemplaryoxide-containing materials may include glasses, glass-ceramics,ceramics, and a combination thereof. Other exemplary organic poreformers can include wax, seeds, and shells, sulfosuccinates,naphthalenes, polyvinyls, ketones, polystyrenes, polyethylenes,polypropylenes, acrylics, benzene-containing polymers, alkyds,polyalkydes, epoxies, phenolics, acetals, and a combination thereof.Suitable inorganic pore formers can include hollow particles, such asbeads, spheres, or the like made of materials such as glass, ceramics,glass-ceramics, or a combination thereof.

Some suitable volatilization agents can include organic materials,naturally occurring materials, or any combination thereof.Volatilization agents can be configured to volatilize at certaintemperatures to form a gas phase. Such volatilization agents may besuitable for the creation of porosity within the body 111 during laterprocessing, which can facilitate controlled cracking of the body andformation of abrasive particles having one or more features of theembodiments herein.

The one or more additives may also include the use of one or moreprecursor additives. A precursor additive is one or more elements orcompounds that may undergo further processing to form an additive. Theone or more precursor additives may be mixed to form one or moreadditives prior to providing the precursor to the body 111. In otherinstances, the one or more precursor additives may be provided to thebody 111, and later processing may facilitate the formation of theadditive within the body 111 (i.e., in-situ additive formation). Forexample, one or more precursor additives can be applied to at least aportion of the body 111, the body can undergo further processing (e.g.,heating), which may facilitate the formation of one or more additiveswithin the body from the one or more precursor additives.

In one embodiment, the additives can be selectively deposited on atleast a portion of the body 111. For example, various techniques may beutilized to selectively deposit the one or more additives (or one ormore precursor additives) to a portion of the body 111, such thataffected portion of the body 111 can have treated areas and untreatedareas. The treated areas are defined as areas where the one or moreadditives have been applied and the untreated areas are defined as areasof the body 111 where the one or more additives have not been applied.The creation of treated and untreated areas on the body may facilitatecontrolled cracking through later processing and the formation ofabrasive particles having one or more features of the embodimentsherein. It will be appreciated that the portions of the body 111 thatmay be affected can be any of the portions described in embodimentsherein as being suitable for modification, including for example, any ofthe exterior surfaces of the body 111. The additives may be applied tothe body such that the treated portions define a controlled distributionas described in the embodiments herein.

After modifying the at least one portion of the body 111, the body 111may undergo further treatment to facilitate formation of the abrasiveparticles. As illustrated in FIGS. 1 and 2, the body 111 may betranslated from the modification zone 120 to a drying zone 140. Withinthe drying zone 140, particular drying conditions can be used tofacilitate controlled cracking of the body 111 and formation ofprecursor abrasive particles 141. In one embodiment, drying is conductedto induce cracking of the body and formation of a plurality of precursorabrasive particles. According to one embodiment, the drying process caninclude controlled cracking conditions configured to fracture the bodyinto a plurality of precursor abrasive particles, wherein the controlledcracking conditions include controlled crack propagation from at leastone crack initiation point.

The drying process may result in the formation of any one or morefeatures of the abrasive particles according to embodiments herein,including such features, but not limited to, microridges, protrusions,depressions, and any combination thereof. According to one embodiment,drying the body can include forming microridges on at least a portion ofa side surface of at least one of the abrasive particles. In anotherembodiment, drying the body can include forming microridges on at leasta portion of a side surface of a majority of the abrasive particles. Instill another embodiment, drying the body can include formingmicroridges on a majority of the side surface of a majority of theabrasive particles. For another embodiment, drying the body can includeforming microridges on at least a portion of a side surface of each ofthe abrasive particles.

As noted herein, the process of modification may define at least onecrack initiation point within the body 111, and the drying process maybe conducted under certain process parameters to control the initiationof the crack and the direction of crack propagation within the body. Theat least one crack initiation point may correspond to one or morefeatures formed within the body 111, including for example, but notlimited to, a protrusion, a depression, an interconnected structure, adiscrete and isolated structure, or any combination thereof. In certaininstances, the at least one crack initiation point can be abutting theone or more features. Moreover, drying may be conducted such that thecrack propagation extends along the length of the one or more features,such that the one or more features substantially guides the direction ofthe crack for at least a portion of the length of the crack. As such, incertain instances, the cracking process results in the formation ofprecursor abrasive particles having a portion of the controlleddistribution of features within the body, such as a major surface of thebody on which the features were formed. It will be appreciated, that theprocess of modifying the body 111 may also include forming a pluralityof crack initiation points, wherein each of the crack initiation pointsis associated with a feature formed in the body 111 or the provision ofan additive within a particular region of the body 111.

According to one embodiment, the drying conditions may be coupled withcertain parameters of the modification process to enable controlledcracking of the body 111 and formation of the desired abrasiveparticles. The process of drying may facilitate controlled cracking ofthe body 111, such that a crack is initiated and grows in the body,extending through the body 111, and separating the body into smallerpieces that form the precursor abrasive particles. The controlledcracking is a distinct process from conventional processes (e.g.,molding, printing, crushing, mechanical sectioning and agitation orvibration), because during controlled cracking the body 111 is torn andfractured under conditions to yield precursor (i.e., green) abrasiveparticles of a targeted shape. In at least one embodiment, the processrelies only on the processes of modifying and drying to alter the body111 into the precursor abrasive particles. The process does notnecessarily require the use of any production tools (e.g., screens ormolds) to achieve the formation of the abrasive particles, and notablyabrasive particles of a targeted size and shape. Such a processrepresents an efficient mechanism for creating abrasive particles with ahigh yield of targeted grains sizes and shapes. Moreover, the resultingabrasive particles are characterized by certain unique features (e.g.,microridges on the side surface and/or protrusions and/or depressions,etc.) due to the forming process.

According to one embodiment, drying can include drying in an environmenthaving a drying temperature of at least 20° C., such as at least 25° C.or at least 30° C. or at least 40° C. or at least 50° C. or at least 60°C. or at least 70° C. or at least 80° C. or at least 90° C. or at least100° C. or at least 110° C. or at least 120° C. or at least 130° C. orat least 140° C. or at least 150° C. or at least 160° C. or at least170° C. or at least 180° C. or at least 190° C. or at least 200° C. orat least 210° C. or at least 220° C. or at least 230° C. or at least240° C. Still, in another non-limiting embodiment, drying can beconducted in an environment at a drying temperature of not greater than250° C., such as not greater than 240° C. or not greater than 230° C. ornot greater than 220° C. or not greater than 210° C. or not greater than200° C. or not greater than 190° C. or not greater than 180° C. or notgreater than 170° C. or not greater than 160° C. or not greater than150° C. or not greater than 140° C. or not greater than 130° C. or notgreater than 120° C. or not greater than 110° C. or not greater than100° C. or not greater than 90° C. or not greater than 80° C. or notgreater than 70° C. or not greater than 60° C. or not greater than 50°C. or not greater than 40° C. or not greater than 30° C. It will beappreciated that drying can be conducted in an environment at a dryingtemperature of within a range including any of the minimum and maximumtemperatures noted above, including but not limited to, within a rangeof at least 20° C. and not greater than 250° C., such as within a rangeincluding at least 50° C. and not greater than 150° C. The temperaturesnoted above can be an average temperature calculated from astatistically relevant number of random positions within a dryingenvironment.

In yet another embodiment, drying can include drying the body in anenvironment having a relative humidity of at least 10%, such as at least20% or at least 30% or at least 40% or at least 50% or at least 60% orat least 70% or at least 80% Still, the relative humidity within theenvironment can be not greater than 90%, such as not greater than 80% ornot greater than 70% or not greater than 60% or not greater than 50% ornot greater than 40% or not greater than 30% or not greater than 20%. Inat least one embodiment, the relative humidity within the environmentcan be within a range including any of the minimum and maximumpercentages noted above, including for example, at least 10% and notgreater than 70% or within a range of at least 10% and not greater than70%. The relative humidity noted above can be an average relativehumidity calculated from a statistically relevant number of randompositions within a drying environment.

In yet another embodiment, drying can include controlling the flow rateof gases (e.g., air) within the drying environment. For example,according to one embodiment, the flow rate of the gas through the dryingenvironment can be at least 0.1 m/s, such as at least 0.2 m/s or atleast 0.5 m/s or at least 0.7 m/s or at least 1 m/s or at least 1.2 m/sor at least 1.5 m/s or at least 1.7 m/s or at least 2 m/s or at least2.2 m/s or at least 2.5 m/s or at least 2.7 m/s or at least 3 m/s or atleast 3.2 m/s or at least 3.5 m/s or at least 3.7 m/s or at least 4 m/sor at least 4.2 m/s or at least 4.5 m/s. Still, in at least onenon-limiting embodiment, the flow rate of the gas (e.g., air, inert gas,oxidizing gas, reducing gas, or any combination thereof) can be notgreater than 5 m/s or not greater than 4.7 m/s or not greater than 4.5m/s or not greater than 4.2 m/s or not greater than 4 m/s or not greaterthan 3.7 m/s or not greater than 3.5 m/s or not greater than 3.2 m/s ornot greater than 3 m/s or not greater than 2.7 m/s or not greater than2.5 m/s or not greater than 2.2 m/s or not greater than 2 m/s or notgreater than 1.7 m/s or not greater than 1.5 m/s or not greater than 1.2m/s or not greater than 1 m/s or not greater than 0.7 m/s or not greaterthan 0.5 m/s. It will be appreciated that the flow rate of the gas orgases can be within a range including any of the minimum and maximumvalues noted above, including for example, within a range including atleast 0.1 m/s and not greater than 5 m/s.

In yet another embodiment, the process of drying can include applyingradiation to the body 111. The radiation may have a wavelength at least0.1 microns or at least 0.5 microns or at least 1 micron or at least 2microns or at least 3 microns or at least 5 microns or at least 10microns or at least 20 microns or at least 50 microns or at least 100microns or at least 200 microns or at least 500 microns or at least 700microns or at least 1 mm. Still, in at least one non-limitingembodiment, the radiation can have a wavelength of not greater than 1 m,such as not greater than 0.8 m or not greater than 0.5 m or not greaterthan 0.1 m, or not greater than 1 cm or not greater than 1 mm or notgreater than 500 microns or not greater than 100 microns or not greaterthan 10 microns. It will be appreciated that the radiation can have awavelength within a range including any of the minimum and maximumvalues noted above. For example, in one embodiment the radiation canhave a wavelength within a range of at least 0.1 microns to not greaterthan 1 mm. Still, in other embodiments, the radiation may have awavelength within a range of at least 1 mm to not greater than 1 m.

In one embodiment, the process of drying to conduct controlled crackingof the body 111 and the formation of precursor abrasive particles may beconducted without the use of other processes, including but not limitedto, mechanical devices (e.g., sectioning devices) intended to contactthe body and separate the body into smaller pieces, ablation processes,vibratory processes, acoustic processes, and the like. In at least oneembodiment, the process of forming the precursor abrasive particles fromthe body 111 is completed using only a drying process and controllingone or more drying conditions including the drying temperature, therelative humidity, drying rate, application of radiation, or anycombination thereof. In at least one embodiment, the process of dryingcan include fracturing of the mixture to create a collection of abrasiveparticles. A collection of abrasive particles is described in moredetail in the embodiments herein.

After forming the precursor abrasive particles 141, the precursorabrasive particles 141 may be translated through additional zones forfurther processing. Alternatively, the precursor abrasive particles 141may be collected in a bin at the end of the belt 109 for furtherprocessing.

In accordance with an embodiment, the process of forming the abrasiveparticles may further comprise a calcining process, wherein theprecursor abrasive particles are subject to a particular heating processto remove water and form calcined abrasive particles. In at least oneembodiment, the calcining temperature used to calcine the precursorabrasive particles can be at least 600° C., such as at least 650° C. orat least 700° C. or at least 750° C. or at least 800° C. or at least850° C. or at least 900° C. or at least 950° C. or at least 1000° C. orat least 1050° C. In still another non-limiting embodiment, thecalcining temperature can be not greater than 1100° C. or not greaterthan 1050° C. or not greater than 1000° C. or not greater than 950° C.or not greater than 900° C. or not greater than 850° C. or not greaterthan 800° C. or not greater than 750° C. or not greater than 700° C. ornot greater than 650° C. It will be appreciated that the calciningtemperature can be within a range including any of the minimum andmaximum values noted above, including for example, within a rangeincluding at least 600° C. and not greater than 1100° C.

After calcination, certain optional processes may be applied to thecalcined abrasive particles. For example, an impregnation process may beused wherein one or more additives may be applied to the calcinedabrasive particles. The additives can include any of the additivesdescribed in embodiments herein, including but not limited to, one ormore dopants.

After conducting calcination, the calcined abrasive particles may besintered to form abrasive particles. Sintering of the precursor abrasiveparticles 141 may be utilized to densify the particles. In a particularinstance, the sintering process can facilitate the formation of ahigh-temperature phase of the ceramic material. For example, in oneembodiment, the calcined abrasive particles may include alumina andsintering is conducted to form a high-temperature phase of alumina, suchas alpha alumina. In at least one embodiment, sintering may be conductedat a sintering temperature within a range including at least 1100° C. tonot greater than 2000° C. The duration of sintering at the sinteringtemperature may be within a range including at least 5 minutes to notgreater than 10 hours.

Non-shaped abrasive particles are generally formed through differentprocesses as disclosed herein and generally have different shapeattributes. For example, non-shaped abrasive particles are typicallyformed by a comminution process, wherein a mass of material is formedand then crushed and sieved to obtain abrasive particles of a certainsize. However, a non-shaped abrasive particle will have a generallyrandom arrangement of the surfaces and edges, and generally will lackany recognizable two-dimensional or three dimensional shape in thearrangement of the surfaces and edges around the body. Moreover,non-shaped abrasive particles of the same group or batch generally lacka consistent shape with respect to each other, such that the surfacesand edges are randomly arranged when compared to each other. Therefore,non-shaped grains or crushed grains have a significantly lower shapefidelity compared to shaped abrasive particles.

The abrasive particles formed through embodiments herein can becontrolled-height abrasive particles having controlled two-dimensionalshapes as viewed top down in a plane of the length and width of theparticle. Generally, the abrasive particles of the embodiments hereincan have two or more surfaces, such as the first and second majorsurfaces that can be substantially parallel to each other and which mayinclude features as disclosed in the embodiments herein. Notably, thearrangement of the first and second major surfaces extending parallel toeach other and defining the length and width of the body generally givethe particles a planar shape and a controlled height. The body of theabrasive particles may further include a side surface extending betweenthe first and second major surfaces. The side surface can have variouscontours depending upon the processing conditions used to form theparticles. Notably, as described herein, the process can be used to forma batch of abrasive particles, wherein the batch can include two or moredifferent shapes of abrasive particles.

FIG. 5 includes a perspective view illustration of a shaped abrasiveparticle. Shaped abrasive particles are known to have been made throughvarious prior art processes, including for example, molding, printing,and the like. The shaped abrasive particle 500 can include a body 501including a major surface 502, a major surface 503, and a side surface504 extending between the major surfaces 502 and 503. As illustrated inFIG. 5, the body 501 of the shaped abrasive particle 500 is athin-shaped body, having a generally equilateral triangular shape,wherein the major surfaces 502 and 503 are larger than the side surface504. Moreover, the body 501 can include an axis 510 extending from apoint to a base and through the midpoint 550 on the major surface 502.The axis 510 can define the longest dimension of the major surfaceextending through the midpoint 550 of the major surface 502, which maybe the length or width of the body depending on the geometry, but in theillustrated embodiment of FIG. 5 defines the width. The body 501 canfurther include an axis 511 defining a dimension of the body 501extending generally perpendicular to the axis 510 on the same majorsurface 502, which in the illustrated embodiment of an equilateraltriangle defines the length of the body 501. Finally, as illustrated,the body 501 can include a vertical axis 512, which in the context ofthin shaped bodies can define a height (or thickness) of the body 501.For thin-shaped bodies, the length of the axis 510 is equal to orgreater than the vertical axis 512. As illustrated, the height 512 canextend along the side surface 504 between the major surfaces 502 and 503and perpendicular to the plane defined by the axes 510 and 511. Shapedabrasive particles are generally formed to remove irregularities fromthe shape, such that each of the shaped abrasive particles within abatch has generally the same size and shape with respect to each other.

FIG. 5 includes an illustration of a shaped abrasive particle having atwo-dimensional shape as defined by the plane of the upper major surface502 or major surface 503, which has a generally triangulartwo-dimensional shape, such as an equilateral triangle.

FIG. 6 includes an illustration of an elongated particle, which is anon-shaped abrasive particle. The elongated abrasive particle can be anon-shaped abrasive particle having a body 651 and a longitudinal axis652 defining the longest dimension of the particle, a lateral axis 653extending perpendicular to the longitudinal axis 652 and defining awidth of the particle. Furthermore, the elongated abrasive particle mayhave a height (or thickness) as defined by the vertical axis 654, whichcan extend generally perpendicular to a plane defined by the combinationof the longitudinal axis 652 and lateral axis 653. As furtherillustrated, the body 651 of the elongated, non-shaped abrasive particlecan have a generally random arrangement of edges 655 extending along anddefining the exterior surface of the body 651. Moreover, the non-shapedabrasive particle does not have a readily identifiable arrangement ofsurfaces or surfaces having a readily identifiable shape and/orarrangement relative to each other.

As will be appreciated, the elongated abrasive particle can have alength defined by the longitudinal axis 652, a width defined by thelateral axis 653, and a vertical axis 654 defining a height. As will beappreciated, the body 651 can have a primary aspect ratio oflength:width such that the length is greater than the width.Furthermore, the length of the body 651 can be greater than or equal tothe height. Moreover, the width of the body 651 can be greater than orequal to the height 654.

FIG. 7A includes a perspective view illustration of a controlled heightabrasive particle according to an embodiment (CHAP). As illustrated, theCHAP 700 can include a body 701 including a first major surface 702, asecond major surface 703, and a side surface 704 extending between thefirst and second major surfaces 702 and 703. As illustrated in FIG. 7A,the body 701 can have a thin, relatively planar shape, wherein the firstand second major surfaces 702 and 703 are larger than the side surface704 and substantially parallel to each other. Moreover, the body 701 caninclude an axis 710, which is the longest dimension on the first majorsurface 710 and defines the length. The body 701 can further include anaxis 711 defining a second longest dimension of the body 701 on thefirst major surface 702, which extends perpendicular to the axis 710 anddefines the width of the body 701. Finally, as illustrated, the body 701can include a vertical axis 712, which can define a height (orthickness) of the body 701. For thin-shaped bodies, the length of theaxis 710 can be equal to or greater than the vertical axis 712. Asillustrated, the height defined by the vertical axis 712 can extendalong the side surface 704 between the first and second major surfaces702 and 703 in a direction generally perpendicular to the plane definedby the axes 710 and 711. It will be appreciated that reference herein tolength, width, and height of the abrasive particles may be referenced toaverage values taken from a suitable sampling size of abrasive particlesof a batch of abrasive particles. The body can further include amidpoint 713 on the first major surface 102 of the body, which generallydefines the point within the center of the first major surface 702.

As further illustrated in FIG. 7A, the body 701 can have a side surface704 having a generally recognizable irregular polygonal (heptagon)two-dimensional shape as viewed in the plane of the first or secondmajor surfaces 702 or 703. An irregular polygonal shape is one in whichall sides are not of equal length to each other. Notably, the body 701has six external corners 721, 722, 723, 724, 725, and 726 (721-726). Theexternal corners 721-726 are portions that would cause significantdeflection of an imaginary rubber band around the side surface 704 ofthe body 701 by at least 10 degrees or greater. Notably, while the body701 has readily identifiable external corners 721-726 and seven sidesurface portions 731, 732, 733, 734, 735, 736, and 737 (731-737)extending between the external corners 721-726, the side surfaceportions 731-737 can have a substantial waviness within the contours,such that the side surface portions 731-737 are not completely planar.Moreover, the edges joining the side surface portions 731-737 to thefirst and second major surfaces 702 and 703 can have some irregularcontours.

It will be appreciated that the CHAP are not so limited and can includeother two-dimensional shapes. For example, the abrasive particles of theembodiments herein can include particles having a body with atwo-dimensional shape as defined by a major surface of the body from thegroup of shapes including polygons, irregular polygons, irregularpolygons including arcuate or curved sides or portions of sides, complexshapes having a combination of polygons shapes, star shapes, shapes witharms extending from a central region (e.g., cross-shaped bodies) and acombination thereof. The processes disclosed herein can be used to formshaped abrasive particles having the features described herein.

FIG. 7B includes a perspective view illustration of another abrasiveparticle according to an embodiment. Notably, the abrasive particle 750has is a controlled height abrasive particle (CHAP) having a body 751including a first major surface 752, a second major surface 753, and aside surface 754 extending between the first and second major surfaces752 and 753. As illustrated in FIG. 7B, the body 751 can have a thin,relatively planar shape, wherein the first and second major surfaces 752and 753 are larger than the side surface 754 and substantially parallelto each other. Moreover, the body 751 can include an axis 761, which isthe longest dimension on the first major surface 752 and defines thelength of the body 751. The body 751 can further include an axis 762defining a second longest dimension of the body 701 on the first majorsurface 702, which extends perpendicular to the axis 761 and defines thewidth of the body 751. Finally, as illustrated, the body 751 can includea vertical axis 763, which can define a height (or thickness) of thebody 701. For thin-shaped bodies, the length of the axis 761 can beequal to or greater than the vertical axis 763. As illustrated, theheight defined by the vertical axis 763 can extend along the sidesurface 754 between the first and second major surfaces 752 and 753 in adirection generally perpendicular to the plane defined by the axes 761and 762. It will be appreciated that reference herein to length, width,and height of the abrasive particles may be referenced to average valuestaken from a suitable sampling size of abrasive particles of a batch ofabrasive particles.

As further illustrated, the body 751 of the abrasive particle 750 canhave a side surface 754 having an irregular two-dimensional shape asviewed in the plane of the first or second major surfaces 752 or 753. Anirregular two-dimensional shape is one in which the shape does not havea recognizable shape, such as a polygonal shape. The irregulartwo-dimensional shape is characterized by a side surface 754 that canhave a random or unpredictable contour. Such an abrasive particle can beformed according to the processes of the embodiments herein. The body751 can have seven external corners 771, 772, 773, 774, 775, 776, and777 (771-777). The external corners 771-777 are portions that wouldcause significant deflection of an imaginary rubber band around the sidesurface 754 of the body 751 by at least 10 degrees or greater.

FIG. 7C includes a top-down view illustration of an abrasive particleaccording to an embodiment. FIG. 7D includes a side view illustration ofa portion of a coated abrasive according to an embodiment. Asillustrated, the body 781 of the abrasive particle can have a polygonaltwo-dimensional shape as viewed top down. The body 781 can have aquadrilateral two-dimensional shape, and more specifically, a righttrapezoid two-dimensional shape. The shape of the body 781 includes aside surface portion 782 that is angled to the adjoining side surfaceportions to create an acute angle 783 and obtuse angle 784 between theside surface portion 782 and abutting side surface portions. Asillustrated in FIG. 7D, the shape of the particles 791 and 792 may beadvantageous in the context of coated abrasives, since there aremultiple orientations of the particles 791 and 792 where a point of theparticles is pointing away from the backing 794. For example, in theorientation of the abrasive particle 791, the tilted surface 793 of theabrasive particle 791 is furthest from the backing 794 and the basesurface 795 is closest to the backing 794. Thus the point 796 isfurthest from the backing 794 and presents a suitable point on theabrasive particle 796 to initiate material removal operations. Regardingthe orientation of the abrasive particle 792, the tilted surface 799 ofthe abrasive particle 792 is closest to the backing 794 and the basesurface 797 is furthest from the backing 794. Thus the point 798 isfurthest from the backing 794 and presents a suitable point on theabrasive particle 792 to initiate material removal operations.

According to any of the abrasive particles of the embodiments herein,the body of the abrasive particle can have a primary aspect ratio oflength:width that can be at least 1.1:1, such as at least 1.2:1 or atleast 1.5:1 or at least 1.8:1 or at least 2:1 or at least 3:1 or atleast 4:1 or at least 5:1 or at least 6:1 or even at least 10:1. Inanother non-limiting embodiment, the body can have a primary aspectratio of length:width of not greater than 100:1, such as not greaterthan 50:1 or not greater than 10:1 or not greater than 6:1 or notgreater than 5:1 or not greater than 4:1 or not greater than 3:1 or evennot greater than 2:1. It will be appreciated that the primary aspectratio of the body can be with a range including any of the minimum andmaximum ratios noted above.

Furthermore, the body of any of the shaped abrasive particles of theembodiments herein can have a secondary aspect ratio of width:heightthat can be at least 1.1:1, such as at least 1.2:1 or at least 1.5:1 orat least 1.8:1 or at least 2:1 or at least 3:1 or at least 4:1 or atleast 5:1 or at least 8:1 or even at least 10:1. Still, in anothernon-limiting embodiment, the secondary aspect ratio width:height can benot greater than 100:1, such as not greater than 50:1 or not greaterthan 10:1 or not greater than 8:1 or not greater than 6:1 or not greaterthan 5:1 or not greater than 4:1 or not greater than 3:1 or even notgreater than 2:1. It will be appreciated the secondary aspect ratio ofwidth:height can be with a range including any of the minimum andmaximum ratios of above.

In another embodiment, the body of any of the abrasive particles canhave a tertiary aspect ratio of length:height that can be at least1.1:1, such as at least 1.2:1 or at least 1.5:1 or at least 1.8:1 or atleast 2:1 or at least 3:1 or at least 4:1 or at least 5:1 or at least8:1 or even at least 10:1. Still, in another non-limiting embodiment,the tertiary aspect ratio length:height can be not greater than 100:1,such as not greater than 50:1 or not greater than 10:1 or not greaterthan 8:1 or not greater than 6:1 or not greater than 5:1 or not greaterthan 4:1 or not greater than 3:1. It will be appreciated that thetertiary aspect ratio can be with a range including any of the minimumand maximum ratios and above.

The abrasive particles of the embodiments herein can have a bodyincluding a crystalline material, and more particularly, apolycrystalline material. Notably, the polycrystalline material caninclude abrasive grains. In one embodiment, the body of the abrasiveparticle can be essentially free of an organic material, including forexample, a binder. In at least one embodiment, the abrasive particlescan consist essentially of a polycrystalline material.

The abrasive grains (i.e., crystallites) contained within the body ofthe abrasive particles may have an average grain size that is generallynot greater than 20 microns, such as not greater than 18 microns or notgreater than 16 microns or not greater than 14 microns or not greaterthan 12 microns or not greater than 10 microns or not greater than 8micron or not greater than 5 microns or not greater than 2 microns ornot greater than 1 micron or not greater than 0.9 microns or not greaterthan 0.8 microns or not greater than 0.7 microns or even not greaterthan 0.6 microns. Still, the average grain size of the abrasive grainscontained within the body of the abrasive particles can be at least 0.01microns, such as at least 0.05 microns or at least 0.06 microns or atleast 0.07 microns or at least 0.08 microns or at least 0.09 microns orat least 0.1 microns or at least 0.12 microns or at least 0.15 micronsor at least 0.17 microns or at least 0.2 microns or even at least 0.5microns. It will be appreciated that the abrasive grains can have anaverage grain size within a range including any of the minimum andmaximum values noted above.

In accordance with an embodiment, the body of the abrasive particle canhave an average particle size, as measured by the largest dimensionmeasurable on the body (i.e., the length), of at least 100 microns. Infact, the body of the abrasive particle can have an average particlesize of at least 150 microns, such as at least 200 microns or at least300 microns or at least 400 microns or at least 500 microns or at least500 microns or at least 600 microns or at least 800 microns or even atleast 900 microns. Still, the body of the abrasive particle can have anaverage particle size that is not greater than 5 mm, such as not greaterthan 3 mm or not greater than 2 mm or even not greater than 1.5 mm. Itwill be appreciated that the body of the abrasive particle can have anaverage particle size within a range including any of the minimum andmaximum values noted above.

In yet another embodiment, the particulate material can have a bodyhaving an average particle size, which may be selected from a group ofpredetermined sieve sizes. For example, the body can have an averageparticle size of not greater than about 5 mm, such as not greater thanabout 3 mm, not greater than about 2 mm, not greater than about 1 mm, oreven not greater than about 0.8 mm. Still, in another embodiment, thebody may have an average particle size of at least about 0.1 microns orat least 1 micron or at least 0.1 mm or at least 0.5 mm. It will beappreciated that the body may have an average particle size within arange between any of the minimum and maximum values noted above.

Particles for use in the abrasives industry are generally graded to agiven particle size distribution before use. Such distributionstypically have a range of particle sizes, from coarse particles to fineparticles. In the abrasive art, this range is sometimes referred to as a“coarse”, “control”, and “fine” fractions. Abrasive particles gradedaccording to abrasive industry accepted grading standards specify theparticle size distribution for each nominal grade within numericallimits. Such industry accepted grading standards (i.e., abrasiveindustry specified nominal grade) include those known as the AmericanNational Standards Institute, Inc. (ANSI) standards, Federation ofEuropean Producers of Abrasive Products (FEPA) standards, and JapaneseIndustrial Standard (JIS) standards. ANSI grade designations (i.e.,specified nominal grades) include: ANSI 4, ANSI 6, ANSI 8, ANSI 16, ANSI24, ANSI 36, ANSI 40, ANSI 50, ANSI 60, ANSI 80, ANSI 100, ANSI 120,ANSI 150, ANSI 180, ANSI 220, ANSI 240, ANSI 280, ANSI 320, ANSI 360,ANSI 400, and ANSI 600. FEPA grade designations include P8, P12, P16,P24, P36, P40, P50, P60, P80, P100, P120, P150, PI 80, P220, P320, P400,P500, P600, P800, P1000, and P1000. JIS grade designations include JIS8,JIS12, JIS 16, JIS24, JIS36, JIS46, JIS54, JIS60, JIS80, JIS 100,JIS150, JIS180, JIS220, JIS240, JIS280, JIS320, JIS360, JIS400, JIS600,JIS800, JIS 1000, JIS 1500, JIS2500, JIS4000, JIS6000, JIS8000, andJIS10,000. Alternatively, the abrasive particles can graded to a nominalscreened grade using U.S.A. Standard Test Sieves conforming to ASTM E-11 “Standard Specification for Wire Cloth and Sieves for TestingPurposes.” ASTM E-1 1 prescribes the requirements for the design andconstruction of testing sieves using a medium of woven wire clothmounted in a frame for the classification of materials according to adesignated particle size. A typical designation may be represented as−18+20 meaning that the particles pass through a test sieve meeting ASTME-1 1 specifications for the number 18 sieve and are retained on a testsieve meeting ASTM E-1 1 specifications for the number 20 sieve. Invarious embodiments, the particulate material can have a nominalscreened grade comprising: −18+20, −20/+25, −25+30, −30+35, −35+40,−40+45, −45+50, −50+60, −60+70, −70/+80, −80+100, −100+120, −120+140,−140+170, −170+200, −200+230, −230+270, −270+325, −325+400, −400+450,−450+500, or −500+635. Alternatively, a custom mesh size could be usedsuch as −90+100. The body of the particulate material may be in the formof a shaped abrasive particle, as described in more detail herein.

Some suitable materials for use in the body of the abrasive particle caninclude of nitrides, oxides, carbides, borides, oxynitrides, oxyborides,oxycarbides, carbon-based materials, diamond, naturally occurringminerals, rare-earth-containing materials, natural minerals, syntheticmaterials, or any combination thereof. In particular instances, theabrasive particles can include an oxide compound or complex, such asaluminum oxide, zirconium oxide, titanium oxide, yttrium oxide, chromiumoxide, strontium oxide, silicon oxide, magnesium oxide, rare-earthoxides, or any combination thereof. In one particular embodiment, thebody can include at least 95 wt % alumina for the total weight of thebody. In at least one embodiment, the body can consist essentially ofalumina. Still, in certain instances, the body can include not greaterthan 99.5 wt % alumina for the total weight of the body. In accordancewith an embodiment, the body may consist essentially of alpha alumina.In certain instances, the body may be formed such that it includes notgreater than about 1 wt % of any low-temperature alumina phases. As usedherein, low temperature alumina phases can include transition phasealuminas, bauxites or hydrated alumina, including for example gibbsite,boehmite, diaspore, and mixtures containing such compounds and minerals.Certain low temperature alumina materials may also include some contentof iron oxide. Moreover, low temperature alumina phases may includeother minerals, such as goethite, hematite, kaolinite, and anastase.

Moreover, in particular instances, the body of the abrasive particlescan be formed from a seeded sol-gel. In at least one embodiment, thebody of any of the abrasive particles of the embodiments herein may beessentially free of iron, rare-earth oxides, and a combination thereof.Reference herein to a body having a certain features (e.g., composition)will also be understood to refer to a batch of abrasive particles thatcan have the same feature (e.g., composition).

In accordance with certain embodiments, certain abrasive particles canbe compositional composites, such that at least two different types ofgrains are contained within the body of the abrasive particle. It willbe appreciated that different types of grains are grains havingdifferent compositions with regard to each other. For example, the bodyof the abrasive particle can be formed such that it includes at leasttwo different types of grains, wherein the types of grains are selectedfrom the group of nitrides, oxides, carbides, borides, oxynitrides,oxyborides, oxycarbides, carbon-based materials, diamond, naturallyoccurring minerals, rare-earth-containing materials, natural minerals,synthetic materials, and a combination thereof.

The body of the abrasive particles may include additives, such asdopants, which may be in the form of elements or compounds (e.g.,oxides). Certain suitable additives can include any of the materialsdescribed herein. The body of an abrasive article may include a specificcontent of one or more additives (e.g., dopant). For example, the bodymay include not greater than about 30 wt % additives for the totalweight of the body. In still other embodiments, the amount of additivesmay be less, such as not greater than about 25 wt % or not greater thanabout 20 wt % or not greater than about 18 wt % or not greater thanabout 15 wt % or not greater than about 12 wt % or not greater thanabout 10 wt % or not greater than about 8 wt % or not greater than 5 wt% or not greater than 2 wt %. Still, the amount of additives can be atleast about 0.5 wt % for a total weight of the body, such as at leastabout 1 wt %, at least about 2 wt % or at least about 3 wt % or at leastabout 4 wt % or at least about 5 wt % or at least about 8 wt % or evenat least about 10 wt %. It will be appreciated that the amount ofadditive within the body may be within a range including any of theminimum and maximum percentages noted above.

The body of the abrasive particle may be particularly dense. Forexample, the body may have a density of at least about 95% theoreticaldensity, such as at least about 96% or even at least about 97%theoretical density.

FIG. 8A includes a top-down image of an abrasive particle according toan embodiment. As illustrated, the abrasive particle 800 includes a body801 including a first major surface 802, a second major surface 803, anda side surface 804 extending between the first and second major surfaces802 and 803. As illustrated in FIG. 8A, the body 801 can have a thin,relatively planar shape, wherein the first and second major surfaces 802and 803 are larger than the side surface 804. The body 801 may have asubstantially quadrilateral two-dimensional shape as viewed top-down inthe plane of the first major surface 802.

The body 801 can have a side surface 804 that can include multiple sidesurface portions that are separated from each other by exterior cornersof the body. The first side surface portion 813 can define a fraction ofthe side surface 804 that can be disposed between a first externalcorner 815 and a second external corner 816. As illustrated andaccording to an embodiment, the first side surface portion 813 can be afraction of the total length of the side surface 804 defining theperimeter of the body 801.

According to one embodiment, the body 801 can include a plurality ofside surface portions, wherein each of the side surface portions extendfor a length of at least 5% of a total length of the body, such as atleast 10% or at least 15% or at least 20% or at least 25%. In anothernon-limiting embodiment, each of the side surface portions can extendfor a length of not greater than 80% of a length of the body, such asnot greater than 70% or not greater than 60% or not greater than 50% ornot greater than 40% or not greater than 30%. It will be appreciatedthat the length of the side surface portions can be within a rangeincluding any of the minimum and maximum percentages noted above.

As further illustrated in FIG. 8A, the body 801 can include one or morefeatures arranged on the first major surface 802 relative to one or moreside surface portions of the side surface 804. As further illustratedand according to one embodiment, the first major surface 802 can furtherinclude a first side surface region 812 disposed between the first sidesurface portion 813 and a first protrusion 811. The first protrusion 811can be abutting the first side surface region 812 and the first sidesurface portion 813. The first protrusion 811 can extend along the firstside surface portion 813 and the first sides surface region 812. Asillustrated, the first protrusion 811 can define a raised portion in theupper surface extending vertically above the height of the first majorsurface 802, the first side surface region 812, and/or an untexturedregion 850 extending through a central region 851 of the body 801. Thefirst protrusion 811 may be formed during the modification process. Forexample, the first protrusion 811 can be a protrusion that can be aresult of moving of the mixture to form a nearby depression during themodification process. Alternatively, the first protrusion 811 can beresult due to adhesion between the form and the mixture forming thebody, such that upon removal of the form from the body, a portion of thebody adheres to the form and is pulled upward to create the firstprotrusion 811.

In at least one embodiment, the first protrusion 811 can extend for afraction of the total length of the side surface 804 defining theperimeter of the body 801. In one particular embodiment, the firstprotrusion 811 can extend for at least 30% of the total length of thefirst side surface portion 813, which is measured as the distancebetween the first external corner 815 and the second external corner816. In another embodiment, the first protrusion 811 can extend for atleast 40% of the total length of the first side surface portion 813 orat least 50% or at least 60% or at least 70% or at least 80% or even atleast 90% of the total length of the first side surface portion 813. Inone particular embodiment, the first protrusion 811 can extend parallelto each other for the entire length of the first side surface portion813. Still, in another non-limiting embodiment, the first protrusion 811can extend for not greater than 99% of the total length of the firstside surface portion 813, such as not greater than 95% or not greaterthan 90% or not greater than 80% or not greater than 70% or not greaterthan 60% or not greater than 50% or not greater than 40% or not greaterthan 30% of the total length of the first side surface portion 813. Itwill be appreciated that the first protrusion 811 can extend for lengthwithin a range including any of the minimum and maximum percentagesnoted above.

According to one embodiment, the first major surface 802 surface caninclude the untextured region 850 that extends through the centralregion 851 of the body. The untextured region 850 can include themidpoint 852 of the first major surface 802 of the body 801. Notably,the first protrusion 811 can be abutting a portion the untextured region850.

Notably, in certain instances, the features (e.g., depressions andprotrusions) on the first major surface 802 can be positioned near theperimeter of the body 801, such that the body 801 includes at least oneuntextured region 850 within the central region 851 of the body. Still,in at least one embodiment, at least a portion of the untextured region850 can be abutting a portion of the side surface (e.g., the fourth sidesurface portion 843), such that there are no features interveningbetween the untextured region 850 and at least one portion of the sidesurface. In another embodiment, the first protrusion 811 can be spacedapart from the untextured region 850 of the first major surface 802.

In yet another embodiment, the untextured region 850 may have atwo-dimensional shape that is substantially the same as thetwo-dimensional shape of the body 801. For example, as illustrated inFIG. 8A, the body 801 can have a generally quadrilateral shape asdefined by the perimeter of the side surface 804, and the untexturedregion 850 can also have a generally quadrilateral shape. It will beappreciated that in certain instances, the body 801 can have a generallyrecognizable two-dimensional polygonal shape, and the untextured region850 can have the same generally recognizable two-dimensional polygonalshape as viewed top down in a plane defined by the length and width ofthe body. Still, other instances, the two-dimensional shape of theuntextured region 850 and the two-dimensional shape of the body 801 canbe different compared to each other.

In at least one embodiment, the untextured region 850 can define asignificant portion of the first major surface 802, including forexample, at least a majority of the surface area of the first majorsurface 802. In at least one embodiment, the untextured region 850 canoccupy at least 10%, such as at least 20% or at least 30% or at least40% or at least 50% or at least 60% or at least 70% or even at least 80%of the total surface area of the first major surface. Such an evaluationmay be made by viewing the particle using an optical microscope at asuitable magnification (e.g., as shown in FIG. 8A) and using imaginganalysis software (e.g., ImageJ) to measure the surface area of thefirst major surface 802 and the surface area of the untextured region850. In one non-limiting embodiment, the untextured region 850 canoccupy not greater than 95% of the surface area of the first majorsurface 802, such as not greater than 90% or not greater than 80% or notgreater than 70% or not greater than 60% or not greater than 50% or notgreater than 40% or not greater than 30%. It will be appreciated thatthe untextured region 850 can occupy a percentage of the surface area ofthe first major surface 850 within a range including any of the minimumand maximum values noted above.

The untextured region 850 may have a notably distinct waviness and/orsurface roughness. For example, the untextured region 850 can have awaviness (Rw) that is distinct from the waviness within the region ofthe first major surface 802 associated with the first depression 811 andthe first protrusion 812. Moreover, in at least one embodiment, theuntextured region 850 can have a surface roughness (Ra) that is distinctfrom the surface roughness of the first major surface 802 associatedwith the first protrusion 811.

In certain instances, any of the features in the first major surface 802can abut the untextured region 850. For example, the first protrusion811 can abut the untextured region 850. The untextured region is aregion that is absent the features (e.g., protrusions and/ordepressions) formed during the process of modifying the body. Theuntextured region 850 can have some surface contours, such as acurvature (e.g., concave curvature), but is generally absent thefeatures formed in the body near the side surface portions. Moreover, incertain embodiments, the untextured region 850 may have a substantiallyplanar contour.

According to another embodiment, the first side surface portion 813 andthe first protrusion 811 can have substantially the same contour asviewed in the plane of the first major surface 802. For example, asillustrated in FIG. 8A, the first side surface portion 813 and the firstprotrusion 811 can have a generally linear shape and extend parallel toeach. In other embodiments, the first side surface portion 813 may havea significantly distinct contour compared to the contour of the firstprotrusion 811.

As further illustrated in FIG. 8A, the body 801 can have a second sidesurface portion 823 that is distinct from the first side surface portion813. In particular, the second side surface portion 823 can be separatedfrom the first side surface portion by at least one external corner,such as the second external corner 816. The second side surface portion823 can extend between the second external corner 816 and a thirdexternal corner 817. As illustrated in FIG. 8A, the first side surfaceportion 813 can be abutting one side of the second external corner 816and the second side surface portion 823 can be abutting the secondexternal corner 816 opposite the first side surface portion 813. Anexternal corner can be defined according to the hypothetical rubber bandtest, wherein the external corner is any corner on the side surface 804around which a rubber band would be significantly deflected (e.g.,defining an angle of deflection of at least 10 degrees or greater) if itwere wrapped around the side surface of the body 804.

In at least one embodiment, any protrusions or depressions can intersectone or more side surface portions. For example, the first protrusion 811can be formed such that it intersects the second side surface portion823. Moreover, as illustrated in FIG. 8A, the first protrusion 811 canintersect the second external corner 816.

The first major surface 802 can include a second protrusion 821extending in a direction parallel to the second side surface portion823. As illustrated and according to an embodiment, the second sidesurface portion 823 can be a fraction of the total length of the sidesurface 804 defining the perimeter of the body 801. As furtherillustrated and according to one embodiment, the first major surface 802can further include a second side surface region 822 disposed betweenthe second side surface portion 823 and the second protrusion 821. Thesecond side surface region 822 can be abutting and extending along thesecond side surface portion 823.

The second protrusion 821 can be abutting the second side surface region822. As illustrated and according to one embodiment, the secondprotrusion 821 and the second side surface region 822 can extendparallel to each other and parallel to the second side surface portion823. In at least one embodiment, the second protrusion 821 and thesecond side surface region 822 can extend parallel to each other for atleast a portion of the second side surface portion 823. The secondprotrusion 821 and the second side surface region 822 can extend for afraction of the total length of the side surface 804 defining theperimeter of the body 801. In one particular embodiment, the secondprotrusion 821 can extend for at least 30% of the total length of thesecond side surface portion 823, which is measured as the distancebetween the second external corner 816 and the third external corner817. In another embodiment, the second protrusion 821 can extend for atleast 40% of the total length of the second side surface portion 823 orat least 50% or at least 60% or at least 70% or at least 80% or even atleast 90% of the total length of the second side surface portion 813. Inone particular embodiment, the second protrusion 821 can extend for theentire length of the second side surface portion 823. Still, in anothernon-limiting embodiment, the second protrusion 821 can extend for notgreater than 99% of the total length of the second side surface portion823, such as not greater than 95% or not greater than 90% or not greaterthan 80% or not greater than 70% or not greater than 60% or not greaterthan 50% or not greater than 40% or not greater than 30% of the totallength of the second side surface portion 823. It will be appreciatedthat the second protrusion 821 can extend for length within a rangeincluding any of the minimum and maximum percentages noted above.

According to another embodiment, the second side surface portion 823 andthe second protrusion 821 can have substantially the same contourcompared to each other as viewed in the plane of the first major surface802. For example, as illustrated in FIG. 8A, the second side surfaceregion 822 and the second protrusion 821 can have a generally linearshape and extend parallel to each other along the direction of thesecond side surface portion 823. In other embodiments, at least thesecond protrusion 821 and the second side surface region 822 can havesubstantially different contour as viewed in the plane of the firstmajor surface 802. That is, the second side surface portion 823 may havea significantly distinct contour compared to the contour of the secondprotrusion 821 and the second side surface region 822.

According to one embodiment, any of the features on the major surfacesof the body can intersect each other. For example, as illustrated inFIG. 8A, the first protrusion 811 can intersect the second protrusion821. Notably, the first protrusion 811 and the second protrusion 821 canintersect each other proximate to an external corner, such as the secondexternal corner 816, which separate the first side surface portion 813and second side surface portion 823. As further illustrated in FIG. 8A,the second side surface region 822 can intersect and abut the firstprotrusion 811. Moreover, according to one embodiment, the first sidesurface region 812 can intersect and abut the second protrusion 821.

In at least one embodiment, the first major surface 802 may include athird portion of a side surface 833. The third side surface portion 833can be distinct from the first side surface portion 813 and the secondside surface portion 823. In particular, the third side surface portion833 can be separated from the first side surface portion 813 and thesecond side surface portion 823 by at least one external corner.According to the illustrated embodiment of FIG. 8A, the third sidesurface portion 833 can be separated from the first side surface portionby the second and third external corners 816 and 817. The third sidesurface portion 833 can be separated from the second side surfaceportion 823 by the third external corner 817. The third side surfaceportion 833 can extend between the third external corner 817 and afourth external corner 818.

In at least one embodiment, the second protrusion 821 and the secondside surface region 822 can intersect the third side surface portion 833proximate the third external corner 817. In particular, the third sidesurface portion 833 may be distinct from the first and second portionsof the side surface 813 and 823 in that there is no third protrusionextending along the third side surface portion 833. The first majorsurface 802 does include a third side surface region 832 extending alongand abutting the third side surface portion 833. The third side surfaceregion 832 can have any of the features of the other side surfaceregions described herein. The third side surface region 832 may be inthe form of a ridge extending vertically above the surface of theuntextured region 850 and may have any feature of the protrusionsdescribed in embodiments herein. Moreover, as illustrated, the thirdside surface region 832 can be abutting the untextured region 850extending through the central region 851 of the body 801. Additionally,the third side surface region 832 can intersect the second protrusion821 proximate the third external corner 817.

In at least one embodiment, the first major surface 802 may include afourth portion of a side surface 843. The fourth side surface portion843 can be distinct from the first side surface portion 813, the secondside surface portion 823, and the third side surface portion 833. Inparticular, the fourth side surface portion 843 can be separated fromthe first side surface portion 813, the second side surface portion 823,and the third side surface portion 833 by at least one external corner.According to the illustrated embodiment of FIG. 8A, the fourth sidesurface portion 843 can be separated from the first side surface portion813 by the first external corner 815. The fourth side surface portion843 can be separated from the second side surface portion 823 by all ofthe external corners 815, 816, 817 and 818. The fourth side surfaceportion 843 can be separated from the third side surface portion 833 bythe fourth external corner 818. The fourth side surface portion 843 canextend between the fourth external corner 818 and the first externalcorner 815.

In at least one embodiment, the fourth side surface portion 843 can bedistinct from the other portions of the side surface 813, 823, and 833,in that it defines an unfeatured edge 844. The unfeatured edge 844defines a joint between the first major surface 802 and the fourth sidesurface portion 843 and does not include any features, such asprotrusions and/or depressions, which are generally formed during theforming process. More particularly, in one embodiment, the unfeaturededge 844 can abut the untextured region 850 extending through thecentral region 851 of the first major surface 802 of the body 801.Accordingly, there are no intervening features (e.g., protrusions ordepressions) between the untextured region 850 of the central region 851and the fourth side surface portion 843. It will be appreciated that theabrasive particles of the embodiments herein may include one or moreunfeatured edges that can intersect one or more featured edges, whereina featured edge comprises at least one feature (e.g., a protrusion ordepression) extending along a portion of the side surface as describedin embodiments herein.

As further illustrated, certain features from the abutting side surfaceportions can intersect the fourth side surface portion 843. For example,the first protrusion 811 can intersect the fourth side surface portion843 proximate the first external corner 815.

FIG. 8B includes a top-down image of an abrasive particle according toan embodiment. FIG. 8C includes a surface profile plot for a portion ofthe major surface of the abrasive particle of FIG. 8B. FIG. 8D includesa surface profile plot for a portion of the major surface of theparticle of FIG. 8B. The image of FIG. 8B was obtained using a Nanovea3D Surface Profilometer using a white light chromatic aberrationtechnique. For each profile (either at X constant or Y constant), theY-step size was 5.00 μm (in the case of X constant) and the X-step sizewas 5.00 μm (in the case of Y constant). The Z resolution was 7.28 nm.Total probed length depends on the grain size, and is measured using thescale bar provided with the line scans.

As illustrated, the abrasive particle 850 includes a body 851 includinga first major surface 852, a second major surface (not illustrated), anda side surface (not illustrated in the view of FIG. 8B) extendingbetween the first major surface 852 and second major surfaces. Asillustrated in FIG. 8B, the body 851 has a substantially quadrilateraltwo-dimensional shape as viewed top-down in the plane of the first majorsurface 852.

As further illustrated in FIG. 8B, the body 851 can include one or morefeatures arranged on the first major surface 852 relative to one or moreside surface portions of the side surface. For example, the first majorsurface 852 can include a first protrusion 853 extending in a directionparallel to a first side surface portion 854. The first side surfaceportion 854 can define a fraction of the side surface that can bedisposed between a first external corner 855 and a second externalcorner 856. As illustrated and according to an embodiment, the firstside surface portion 853 can be a fraction of the total length of theside surface defining the perimeter of the body. The first protrusion853 can be abutting the first side surface portion 854 and extend alongthe first side surface portion 854. As illustrated, the first protrusion852 can define a raised portion in the first major surface 852 extendingvertically above the height of the first major surface 852 and anuntextured region 890 extending through a central region 891 of the body851. The first protrusion 853 can have any of the features of theprotrusions described in the embodiments herein. The upper surface 852can further include a first side surface region 856 disposed between thefirst protrusion 853 and the first side surface portion 854.

Notably, FIG. 8C includes a surface profile plot of the first majorsurface 852 along the axis 881. The surface profile plot was obtainedusing a Nanovea 3D Surface Profilometer using a white light chromaticaberration technique. For each profile (either at X constant or Yconstant), the Y-step size was 5.00 μm (in the case of X constant) andthe X-step size was 5.00 μm (in the case of Y constant). The Zresolution was 7.28 nm. Total probed length depends on the grain size,and is measured using the scale bar provided with the line scans.

As illustrated in the plot, the first protrusion 853 extends above thefirst major surface 852. As illustrated, the first protrusion 853 can bein direct contact with the untextured region 890. The first protrusion853 can extend along the entire length of the first side surface portion854 between the first external corner 855 and the second external corner856. Moreover, the first protrusion 853 can have substantially the samecontour as viewed top-down (as provided in FIG. 8B) as the first sidesurface portion 854. The first protrusion 853 and the first side surfaceportion 854 can have an arcuate contour as illustrated in FIG. 8B. Itshould be noted that not all abrasive particles of the embodimentsherein will include each of the features depicted in certain abrasiveparticles, and the abrasive particles may include different combinationsof certain features.

As further illustrated in FIG. 8B and according to one embodiment, thebody 851 can further include a second protrusion 863 extending above thefirst major surface 852. The second protrusion 863 can extend in adirection parallel to a second side surface portion 864. The second sidesurface portion 864 can define a fraction of the side surface that canbe disposed between the second external corner 856 and a third externalcorner 857. As illustrated and according to an embodiment, the secondside surface portion 863 can be a fraction of the total length of theside surface defining the perimeter of the body 851. The secondprotrusion 863 can be abutting the second side surface portion 864 andextend along the second side surface portion 864. As illustrated, thesecond protrusion 862 can define a raised portion in the first majorsurface 852 extending vertically above the height of the first majorsurface 852 and the untextured region 890 that extends through a centralregion 891 of the body 851. The second protrusion 863 can have any ofthe features of the protrusions described in the embodiments herein. Theupper surface 852 can further include a second side surface region 866disposed between the second protrusion 863 and the second side surfaceportion 864.

Notably, FIG. 8D includes a surface profile plot of the first majorsurface 852 along the axis 882 and was obtained using the same techniqueused to create the plot of FIG. 8C.

According to the illustrated embodiment of FIG. 8B, the secondprotrusion 863 can extend along the entire length of the second sidesurface portion 864 between the second external corner 856 and the thirdexternal corner 857. Moreover, the second protrusion 863 can havesubstantially the same contour as viewed top-down (as provided in FIG.8B) as the second side surface portion 864. The second protrusion 863and the second side surface portion 864 can each have a generally planarcontour and extend in a generally linear direction as illustrated inFIG. 8B. In the illustrated embodiment of FIG. 8B, the first protrusion853 and the second protrusion 863 intersect each other at region 865,which is proximate to the second external corner 856.

The first major surface 852 of the body 851 can further include a firstdepression 867, which can be adjacent to the second protrusion 863 andextend along a majority of the length of the second protrusion 863. Thefirst depression 867 can be positioned between the second protrusion 863and the untextured region 890. The first depression 867 can furtherextend along the direction of the second protrusion 863 and the secondside surface portion 864. Moreover, in the embodiment, of FIG. 8B, thefirst depression 867 can extend in a direction parallel to the secondprotrusion 863 and the second side surface portion 864. Additionally,the second protrusion 863 can be disposed between the second sidesurface portion 864 and the first depression 867.

The second protrusion 863 can further be abutting the first depression867. As illustrated and according to one embodiment, the secondprotrusion 863 and the first depression 867 can extend for a fraction ofthe total length of the side surface defining the perimeter of the body801. In one particular embodiment, the second protrusion 863 and/or thefirst depression 867 can extend for not greater than 30% of the totallength of the second side surface portion 864, which is measured as thedistance between the external corners 856 and 857. In anotherembodiment, the second protrusion 863 and/or the first depression 867can extend parallel to each other for at least 40% of the total lengthof second side surface portion 864 or at least 50% or at least 60% or atleast 70% or at least 80% or even at least 90% of the total length ofthe second side surface portion 864. In one particular embodiment, thesecond protrusion 863 and/or the first depression 867 can extendparallel to each other for the entire length of the second side surfaceportion 864. Still, in another non-limiting embodiment, the secondprotrusion 863 and/or the first depression 867 can extend parallel toeach other for not greater than 99% of the total length of the secondside surface portion 864, such as not greater than 95% or not greaterthan 90% or not greater than 80% or not greater than 70% or not greaterthan 60% or not greater than 50% or not greater than 40% or not greaterthan 30% of the total length of the second side surface portion 864. Itwill be appreciated that the second protrusion 863 and/or the firstdepression 867 can extend parallel to each other for length within arange including any of the minimum and maximum percentages noted above.

It will be appreciated that other abrasive particles can include morethan one depression. For example, particles of the embodiments hereinmay have one or more depressions on the surface, and such depressionscan be associated with and abutting more than one other portions of theupper surface of the body, including for example, one or moreprotrusions, the untextured region, and the like. One or moreprotrusions can be disposed between a depression and a side surfaceportion. Likewise, one or more depressions can be disposed between aprotrusion and the untextured region.

As illustrated in FIG. 8D, the first depression 867 can have a notabledepth that defines a portion of the first major surface 852 that ispositioned vertically below the first major surface associated with theuntextured region 890 and the portion of the first major surface 852associated with the second protrusion 863. As further illustrated, thefirst depression 867 can intersect and abut a portion of the firstprotrusion 853 in the region 868. Notably, the first depression 867 canterminate at the intersection of the first protrusion 853.

As further illustrated in FIG. 8B, the first major surface 852 of thebody 851 can include a third side surface portion 874 extending betweenthe third external corner 857 and a fourth external corner 858. The bodycan further include a fourth side surface portion 884 extending betweenthe fourth external corner 858 and the first external corner 855, suchthat the body can have a generally four-sided shape, wherein the firstside surface portion 854 and the fourth side surface portion 884 have anarcuate contour. The second side surface portion 864 and the third sidesurface portion 874 can have substantially planar contours and extend ina generally linear direction. It should be noted that the second sidesurface portion 864 and the third side surface portion 874 can have someminor irregularities in the contours of the edge.

The first major surface 852 can further include a third protrusion 883located proximate to the fourth external corner 858. The thirdprotrusion 883 can extend for a fraction of the length of the fourthside surface portion 884. As further illustrated in FIG. 8B, the thirdprotrusion 883 can have a rounder shape compared to the first and secondprotrusions 853 and 863. Moreover, the third protrusion 883 can beabutting the untextured region 890.

FIGS. 9A-9E include images of other abrasive particles according toembodiments herein. FIGS. 9A-9E provide details on other features of theabrasive particles of the embodiments herein. For example, FIG. 9Aincludes an abrasive particle 900 including a body 901 having a firstmajor surface 902, a second major surface 903, and a side surface 904extending between the first and second major surfaces 902 and 903. Inparticular, in certain embodiments, a feature may intersect a portion ofa side surface along which that feature extends. For example, the firstmajor surface 902 includes a first protrusion 911 that extends along aportion of the first side surface portion 913. As illustrated, the firstprotrusion 911 can intersect the first side surface portion 913. Asfurther illustrated, the first protrusion 911 can have a differentcontour compared to the first side surface portion 913, which furtherfacilitates the intersection between the first protrusion 911 and thefirst side surface portion 913. In particular, the first depression 911can have a generally linear contour and the first side surface portion913 can have a curved contour including a concave portion that causesthe first side surface portion 913 to intersect the first protrusion911.

FIG. 9B includes an abrasive particle 920 including a body 921 having afirst major surface 922, a second major surface 923, and a side surface924 extending between the first and second major surfaces 922 and 923.In particular, in certain embodiments, an edge between one of the majorsurfaces and the side surface may have an irregular contour definingjagged and sharp regions. For example, the second major surface 923 andthe side surface 924 can be joined at the edge 925, which ischaracterized by an irregular contour defining jagged and sharp regions.

Moreover, in one embodiment, the first major surface 922 can have afirst surface area (A1) and the second major surface 923 can have asecond surface area (A2). According to one embodiment, the first surfacearea can be different than the second surface area. Notably, in at leastone instance, A1 can be less than A2. In more particular instances, thedifference between the first surface area (A1) and the second surfacearea (A2) can be defined by a ratio (A1/A2), wherein A1/A2 can be notgreater than 1, such as not greater than 0.9 or not greater than 0.8 ornot greater than 0.7 or not greater than 0.6 or not greater than 0.5 ornot greater than 0.4 or not greater than 0.3 or not greater than 0.3 ornot greater than 0.2 or not greater than 0.1. Still, in anothernon-limiting embodiment, the ratio (A1/A2) can be at least 0.01, such asat least 0.05 or at least 0.1 or at least 0.2 or at least 0.3 or atleast 0.4 or at least 0.5 or at least 0.6 or at least 0.7 or at least0.8 or even at least 0.9. It will be appreciated that the ratio (A1/A2)can be within a range including any of the minimum and maximum valuesnoted above.

While all of the images of the abrasive particles of FIGS. 8A-8D and9A-9E have included particles having a generally rectangulartwo-dimensional shape, it will be appreciate that any of the featuresdescribed in association with these particles can be applied toparticles having an irregular two-dimensional shape, such irregularplanar abrasive particles.

Moreover, reference herein to any dimensional characteristic (e.g.,length, width, height, etc.) can be reference to a dimension of a singleparticle, a median value, or an average value derived from analysis of asuitable sampling of particles. Unless stated explicitly, referenceherein to a dimensional characteristic can be considered reference to amedian value that is based on a statistically significant value derivedfrom a random sampling of suitable number of particles. Notably, forcertain embodiments herein, the sample size can include at least 10, andmore typically, at least 40 randomly selected particles from a batch ofparticles. A batch of particles may include, but need not necessarily belimited to, a group of particles that are collected from a singleprocess run. In yet another instance, a batch of abrasive particles canbe a group of abrasive particles of an abrasive article, such as a fixedabrasive article. For example, a batch of particles may include anamount of abrasive particles suitable for forming a commercial gradeabrasive product, such as at least about 20 lbs. of particles.

FIG. 15A includes an image of a side surface of an abrasive particleincluding a plurality of microridges according to an embodiment. Asillustrated, the abrasive particle 1500 includes a body 1501 including afirst major surface 1502, a second major surface 1503, and a sidesurface 1504 extending between the first and second major surfaces 1502and 1503. The body 1501 can have a thin, relatively planar shape,wherein the first and second major surfaces 1502 and 1503 are largerthan the side surface 1504.

According to one embodiment, a majority of the side surface can includea plurality of microridges. For example as illustrated in the image ofFIG. 15A, the side surface 1504 includes a plurality of microridges1505. Notably, the plurality of microridges 1505 on the side surface1504 create an entirely distinct appearance and texture compared to asurface in contact with a surface (e.g., a molded) surface asrepresented by the second major surface 1503, which has a planar contourand is free of microridges 1505. In certain instances, the plurality ofmicroridges 1505 create a surface having jagged surface features,representative of an unpolished ceramic surface.

The plurality of microridges 1505 appear to have multiple, distinctmorphologies or types. A first type of microridge can include isolatedmicroridges 1506, which can be defined by microridges extending out theside surface and along the side surface. The isolated microridges 1506can be separated by generally smooth planar regions. The second type ofmicroridge can include scaled microridges 1507, which may have a scaledor layered appearance. Another type of includes expanding microridges,which includes a plurality microridges extending outward from a focalregion. Such microridges are described in accordance with FIG. 17.Without wishing to be tied to a particular theory, the plurality ofmicroridges 1505 appears to be an artifact of the forming processesdescribed in the embodiments herein. Notably, it is thought that theplurality of microridges 1505 is formed during the controlled crackingand fracturing of the body used to form the abrasive particles.Accordingly, the plurality of microridges 1505 may be characterized asconchoidal or subconchoidal fracturing features formed as the body wasfractured into smaller portions that ultimately formed the abrasiveparticles based on the process as described herein. Moreover, it istheorized that the different types of microridges may be associated withdifferent conditions during processing. Such features appear to bedistinct from the side surfaces of particles formed according to otherconventional processes used to form abrasive particles, such as molding,printing, cutting and the like. Region 1508 of the side surface 1504 inFIG. 15A provides a perspective view image of the roughened andirregular features exhibited by the plurality of microridges.

In one embodiment, an abrasive particle can have a side surface, whereinat least 51% of the total surface area of the side surface includes theplurality of microridges 1505. In another embodiment, a greaterpercentage of the side surface 1504 can include the plurality ofmicroridges 1505, including for example, but not limited to, at least52% or at least 54% or at least 56% or at least 58% or at least 60% orat least 62% or at least 64% or at least 66% or at least 68% or at least70% or at least 72% or at least 74% or at least 76% or at least 78% orat least 80% or at least 82% or at least 84% or at least 86% or at least88% or at least 90% or at least 92% or at least 94% or at least 96% orat least 98% or even at least 99% of the total surface area of the sidesurface. In another non-limiting embodiment, not greater than 99% of thetotal surface area of the sides surface 1504 can include the pluralityof microridges 1505, such as not greater than 98% or not greater than96% or not greater than 94% or not greater than 92% or not greater than90% or not greater than 88% or not greater than 86% or not greater than84% or not greater than 82% or not greater than 80% or not greater than78% or not greater than 76% or not greater than 74% or not greater than72% or not greater than 70% or not greater than 68% or not greater than66% or not greater than 64% or not greater than 62% or not greater than60% or not greater than 58% or not greater than 56% or not greater than54% or not greater than 52%. It will be appreciated that the totalsurface area of the side surface covered by the plurality of microridges1505 can be within a range including any of the minimum and maximumpercentages noted above.

As noted in other embodiments, the side surface may include a pluralityof side surface portions, wherein each side surface portion is definedas a portion of the side surface extending between the external cornersof the body. According to one embodiment, at least 45% of the sidesurface portions for a given abrasive particle can include the pluralityof microridges. In still other embodiments, the percentage can begreater, including for example, at least 52% of the side surfaceportions of the body include the plurality of microridges, or at least54% or at least 56% or at least 58% or at least 60% or at least 62% orat least 64% or at least 66% or at least 68% or at least 70% or at least72% or at least 74% or at least 76% or at least 78% or at least 80% orat least 82% or at least 84% or at least 86% or at least 88% or at least90% or at least 92% or at least 94% or at least 96% or at least 98% orat least 99%. In at least one embodiment, all of the side surfaceportions of the side surface for a given abrasive particle can includethe plurality of microridges.

While it will be understood that the two-dimensional shape of the bodyas viewed top-down will determine the number of side surface portionsfor an abrasive particle, in at least one embodiment, the body caninclude at least three side surface portions including the plurality ofmicroridges. In other embodiments, the number of side surface portionsincluding the plurality of microridges can be greater, such as at leastfour or at least five or at least six or at least seven or at leasteight. Still, it will be appreciated that in at least one embodiment, anabrasive particle may be formed such that at least one side surfaceportion does not include the plurality of microridges.

FIG. 15B includes a magnified image of a portion of the abrasiveparticle of FIG. 15A. FIG. 15B more clearly depicts the two differenttypes of microridges that have been observed on the abrasive particlesof the embodiments herein. As depicted, the first type of microridgescan include a plurality of isolated microridges, which can include theisolated microridges 1506 separated from each other by the smooth planarregions 1511. As further illustrated, the isolated microridges 1506 canextend along the side surface in an irregular path. The path of theisolated microridges 1506 may be irregular but characterized by somecoordination when compared to each other. For example, as illustrated inFIG. 15B, the isolated microridges 1506 can extend along the sidesurface in an irregular path, but can have generally the same irregularpath relative to each other. According to one embodiment, at least aportion of a group of isolated microridges 1506, which can be adjacentto each other, can extend in a generally coextensive manner, such thatthey define the same pathway relative to each other, but are separatedby the smooth planar regions 1511. Such an arrangement appears similarto lanes on a highway.

In another embodiment, at least one of the isolated microridges of theplurality of isolated microridges 1506 can be made up of differentregions having different shapes. For example, at least one of theisolated microridges can include a head region 1513 and a tail region1514 connected to and extending from the head region 1513. As depictedand according to one embodiment, the head region 1503 can have a roundedshape. The tail region 1514 can have an elongated shape. In at least oneembodiment, an isolated microridge can include a series of these regionslinked together and separated by one or more gaps 1516. The gaps 1516can define an interruption in the isolated microridges 1506. The gaps1516 can define smooth regions positioned along the irregular path ofthe one or more isolated microridges 1506. In at least one embodiment,the irregular path of an isolated microridge 1506 can include aplurality of gaps 1516, and thus the isolated microridge may becharacterized as a series of isolated microridge portions 1517 extendingalong an irregular path. Any of the isolated microridge portions caninclude a head region and tail region.

The plurality of isolated microridges 1506 may extend along the sidesurface for a significant distance. For example, at least one of theisolated microridges 1506 can extend for at least 10% of the averageheight of the side surface 1504. In other embodiments, the length of oneor more isolated microridges 1506 on the side surface 1504 can be atleast 20% or at least 30% or at least 40% or at least 50% or at least60% or at least 70% or at least 80% or at least 90% or at least 95% ofthe average height of the side surface 1504. In still anothernon-limiting embodiment, the length of one or more isolated microridges1506 on the side surface 1504 can be not greater than 99% or not greaterthan 90% or not greater than 80% or not greater than 70% or not greaterthan 60% or not greater than 50% or not greater than 40% of the averageheight of the side surface. It will be appreciated that the length ofone or more of the isolated microridges 1506 along the side surface 1504can be within a range including any of the minimum and maximumpercentages noted above.

In certain instances, one or more of the plurality of isolatedmicroridges 1506 can have a total length of at least 100 microns, suchas at least 150 microns or at least 200 microns or at least 300 micronsor at least 400 microns. Still, depending upon the height of theabrasive particle, the total length of at least one of the isolatedmicroridges 1506 may be not greater than 2 mm, such as not greater than1 mm or even not greater than 500 mm.

The plurality of isolated microridges 1506 may have a very smallthickness, particularly in the tail region 1514, wherein the thicknessis measured in a direction transverse to the microridge and thedirection defining the length of the microridge. As depicted in FIG.15B, the tail region 1514 of any one of the isolated microridges 1506may have a thickness of less than 10 microns, such as less than 8microns or not greater than 6 microns or not greater than 4 microns ornot greater than 2 microns. Still, it appears that the tail region 1514of the isolated microridges 1506 may have a thickness of at least 0.01microns or at least 0.1 microns. The thickness of the tail region 1514is the maximum thickness measured in the tail region 1514.

The plurality of isolated microridges 1506 may have a thickness in thehead region 1513 that is greater than the thickness in the tail region1514. As depicted in FIG. 15B, the head region of any one of theisolated microridges 1506 may have a thickness of less than 50 microns,such as less than 40 microns or not greater than 30 microns or notgreater than 20 microns. Still, it appears that the head region 1513 ofthe isolated microridges 1506 may have a thickness of at least 1 micronor at least 1 micron. The thickness of the head region 1513 is themaximum thickness measured in the head region 1513 for a given isolatedmicroridge 1514.

As further depicted in FIG. 15B, at least a portion of the plurality ofmicroridges 1505 can include a plurality of scaled microridges 1507. Theplurality of scaled microridges 1507 can have a different morphologycompared to the isolated microridges 1506. As illustrated, the pluralityof scaled microridges 1507 can include a plurality of raised portionswith irregular shapes and wrinkles extending between the raisedportions. More particularly, the plurality of scaled microridges 1507can include one or more primary ridges 1521 defining raised portions anda plurality of wrinkles 1522 extending from the one or more primaryridges 1521. In certain instances, the plurality of wrinkles 1522 canextend between and/or across two or more primary ridges 1521.

According to one embodiment, and as depicted in FIG. 15B, the one ormore primary ridges 1521 of the scaled microridges 1507 can extend alongthe side surface of the body in an irregular path. The irregular pathgenerally includes a random combination of linear and arcuate sectionsjoined together. As further illustrated, the one or more primary ridges1521 can be laterally spaced apart from each other but may have somecoordination relative to each other, such that portions of the primaryridges 1521, including for example, those primary ridges that areadjacent to each other, can extend in a coextensive manner, like theisolated microridges 1506.

In one aspect, the primary ridges 1521 can have any of the features withrespect to size and direction as described in accordance with theisolated microridges. For example, the primary ridges 1521 may extendalong the side surface 1504 for a significant distance. For example, atleast one of the primary ridges 1521 can extend for at least 10% of theaverage height of the side surface 1504. In other embodiments, thelength of one or more primary ridges 1521 on the side surface 1504 canbe at least 20% or at least 30% or at least 40% or at least 50% or atleast 60% or at least 70% or at least 80% or at least 90% or at least95% of the average height of the side surface. In still anothernon-limiting embodiment, the length of one or more primary ridges 1521on the side surface 1504 can be not greater than 99% or not greater than90% or not greater than 80% or not greater than 70% or not greater than60% or not greater than 50% or not greater than 40% of the averageheight of the side surface 1504. It will be appreciated that the lengthof one or more primary ridges 1521 along the side surface 1504 can bewithin a range including any of the minimum and maximum percentagesnoted above.

In certain instances, one or more of the primary ridges 1521 can have atotal length of at least 100 microns, such as at least 150 microns or atleast 200 microns or at least 300 microns or at least 400 microns.Still, depending upon the height of the abrasive particle, the totallength of at least one of the primary ridges 1521 may be not greaterthan 2 mm, such as not greater than 1 mm or even not greater than 500mm. It will be appreciated that the total length of at least one of theprimary ridges 1521 can be within a range including any of the minimumand maximum values noted above.

As further depicted in FIG. 15B, the scaled microridges 1507 can includea plurality of wrinkles 1522, which can extend along the side surface inan irregular pathway from one or more primary ridges 1521. Generally, atleast a significant portion of the plurality of wrinkles 1522 can extendalong a curved path on the side surface of the body. In certaininstances, the wrinkles can define grooves extending along the sidesurface 1504 along an irregular path. Certain embodiments of the scaledridges 1507 may include a greater number of wrinkles 1522 compared tothe number of primary ridges 1521.

As further depicted in FIG. 15B and according to one embodiment, theplurality of wrinkles 1522 can extend in a different direction comparedto one or more primary ridges 1521. For example, the plurality ofwrinkles 1522 may extend from, between, and/or across one or moreprimary ridges 1521. The plurality of wrinkles 1522 may extendtransversely to the length of the primary ridges 1521. The plurality ofwrinkles 1522 may be in the form or grooves extending into the body atthe side surface.

In certain embodiments, the plurality of wrinkles 1522 may define cutsthrough the primary ridges 1521, which may form gaps 1523 or regions ofreduced height in the primary ridges 1521. According to one embodiment,one of more of the primary ridges 1521 can include at least one gap 1523between elongated portions defining the primary ridge 1521. The gap 1523may be associated with and/or connected to one or more wrinkles 1522extending from the gap 1523.

As noted herein, the scaled microridges 1507 can have a scaled or scalyappearance. Unlike the isolated microridges 1506, the scaled microridges1507 appear to have a greater waviness and/or roughness. Moreover, theregion of the side surface having the scaled microridges 1507 can definea region of the side surface having a greater roughness compared to theregion of the side surface including the isolated microridges 1506. Thescaled microridges 1506 and isolated microridges 1507 may also bedistinguished from each other based on one or more other surfacefeatures, including for example, but not limited to, waviness, maximumsurface roughness, and the like.

As further depicted in FIG. 15B, the scaled microridges 1507 can beabutting the isolated microridges 1506. In certain instances, the scaledmicroridges 1507 and isolated microridges 1506 can be coordinated, suchthat the primary ridges 1521 of the scaled microridges 1507 and theisolated microridges 1506 can have portions that are coextensive,despite having an irregular pathway across the side surface of the body.Without wishing to be tied to a particular theory, it is thought thatthe isolated microridges 1506 and scaled microridges 1507 may occur fromthe same process, such as fracturing during formation, but theconditions during formation of the isolated microridges 1506 may differslightly from the conditions during formation of the scaled microridges1507.

FIG. 16 includes an image of a portion of a side surface includingscaled microridges according to an embodiment. As depicted, the scaledmicroridges 1607 can include a plurality of primary ridges 1621extending in an irregular pathway and a plurality of wrinkles 1622extending from, between, and/or across the plurality of primary ridges1621. According to the embodiment depicted in FIG. 16, the scaledmicroridges 1607 can have a layered appearance, such that the surfaceappears to be made of a plurality of layers overlying each other. Itwill be appreciated that the scaled microridges 1607 may not actuallyinclude a plurality of layers, but the morphology of the scaledmicroridges 1607 provides such an appearance.

According to another embodiment, and as illustrated in FIG. 16, thescaled microridges 1607 may include one or more precipice regions 1631.The precipice regions 1631 can include a portion of the primary ridgesor other raised portions of the scaled microridges 1607 that appear torise sharply and away from the side surface and be separated from anunderlying region by a shear face. The precipice regions 1631 mayinclude, but need not necessarily include, an overhang or outcroppingthat may hang in space over the underlying region, like the crest of awave. For example, the precipice region 1631 can include a raisedportion 1632 that extends above an underlying region 1633. The raisedportion 1632 and the underlying region 1633 can be separated from eachother by a shear face 1634.

FIG. 17 includes an image of a side surface of an abrasive particleincluding another type of microridges according to an embodiment. Theabrasive particle 1701 can include a side surface 1702 including aplurality of extending microridges 1703. As depicted, the plurality ofextending microridges 1703 can be a different type of microridgecompared to the isolated and scaled microridges in terms of theirmorphology. For example, as provided in FIG. 17, the plurality ofextending microridges 1703 appears to be extending from a focal region1704. That is, the plurality of extending microridges 1703 appears to bequite elongated, extending for significant distances along the sidesurface 1702 and extending away from a focal region 1704. The pluralityof extending microridges 1703 can include tightly packed microridgescompared to the scaled and isolated types of microridges. That is, theaverage distance between immediately adjacent microridges for theextending microridges 1703, can be smaller than the average distancebetween the isolated microridges or scaled microridges, where theaverage distance is measured as the average of the smallest distancebetween two immediately adjacent ridges. In at least one embodiment, theplurality of extending microridges 1703 can extend in multipledirections from the focal region 1704. Without wishing to be tied to aparticular theory, the plurality of extending microridges 1703 may beformed during a high energy fracturing mode, wherein fracturing isinitiated in the focal region 1704 and extends rapidly outward in alldirections from the focal region 1704, thus facilitating the formationof the plurality of extending microridges 1703. Moreover, the fracturingconditions occurring during the formation of the plurality of extendingmicroridges 1703 may be distinct from the fracturing conditions duringthe formation of other types of microridges, such as the isolated orscaled microridges.

In addition to or as an alternative to any of the features describedherein, the abrasive particles formed through the methods describedherein can have particular features, which may be associated with theside surface or portions of the side surface. FIG. 18 includes a sideview image of an abrasive particle according to an embodiment. FIG. 19includes a magnified image of a portion of the sidewall from FIG. 18.FIG. 20 includes the side view image of FIG. 18 marked for measurementof the height of the body and the second region. In one aspect, the body1801 of the abrasive particle can include a first major surface 1802, asecond major surface 1803 opposite the first major surface 1802, and aside surface 1804 extending between the first major surface 1802 and thesecond major surface 1803. Reference herein to a major surface of anabrasive particle may be reference to a surface that is larger than theother surfaces of the body. However, it is not necessary that one ormore major surfaces always be the surface of the greatest area. In oneembodiment, the side surface 1804 comprises a particular Mean AnisotropyFactor (MAF). The MAF can be associated with a single particle or acollection of particles. The MAF is an analysis technique used tomeasure the unique fracture signature associated with the side surfaceof particles formed according to the embodiments herein. Without wishingto be tied to a particular theory, it is suggested that the combinationof parameters of the methods disclosed herein result in the formation ofshaped abrasive particles with unique textures on portions of thesidewall that can be quantified by the MAF. MAF is measured by analyzinga side surface or portion of a side surface and taking a scanningelectron micrograph image of approximately 1000× magnification with anappropriate contrast and resolution to clearly distinguish the features,such as provided in FIG. 18. Notably, if a portion of the sidewallappears to have greater texture than another portion, the analysisshould be focused in this region (e.g., the region 1806 as provided inFIG. 19). The image is then analyzed with a Fourier Transform accordingto the equations provided below.

The definition of the Fourier Transform (FT) is given below:

${FT}:\left. \left( {u,v} \right)\rightarrow{\sum\limits_{x,{y = 0}}^{N - 1}{{f\left( {x,y} \right)} \cdot e^{{{- j} \cdot 2}{\pi \cdot \frac{{u \cdot x} + {v \cdot y}}{N}}}}} \right.$

It is implied that “f” is the original image and (x,y) its horizontaland vertical axes, and “F” is the Fourier Transform of the originalimage, and (u,v) its axis in the frequency space.

And where j=√−1 and “N” is the size of the original image in pixel.

By definition, we have FTi(FT(f))=f. The Fourier Transform F of theoriginal image “f” can be written as follows:

F=A×e ^(−jφ)

Where;

$A = {{\sqrt{{{Re}(F)}^{2} + {{Im}(F)}^{2}}\mspace{14mu} {and}\mspace{14mu} \phi} = {\tan^{- 1}\frac{{Re}(F)}{{Im}(F)}}}$

We call “A” the magnitude of the Fourier Transform, and φ its phase. Tocalculate MAF we focus on the variable “A”, as it is the magnitude thatcontains the information of interest.

A Principle Component Analysis (PCA) technique is then used to evaluatethe image that is analyzed by the Fourier Transform. The FourierTransform “F” may be considered as a probability distribution. Hence,“F” is normalized as follows:

${p\left( {u,v} \right)} = {{\frac{F\left( {u,v} \right)}{\sum_{u,{v = 1}}^{N}{F\left( {u,v} \right)}}\mspace{14mu} {for}\mspace{14mu} \left( {u,v} \right)} \in {〚{1,N}〛}}$

Now, let

$U = {\begin{pmatrix}u \\v\end{pmatrix}.}$

We compute me covariance COV of U:

COV=E[(U−E(U))×(U−E(U))^(T)]

Where E is defined as:

$E:\left. \begin{pmatrix}u \\v\end{pmatrix}\rightarrow{\sum\limits_{u,{v = 1}}^{N}{{p\left( {u,v} \right)} \times \begin{pmatrix}u \\v\end{pmatrix}}} \right.$

As F is symmetric, it follows that E(U)=0. Hence, we have:

COV=E(U×U ^(T))

COV is symmetric and positive-definite matrix. Hence, it can be writtenas:

${COV} = {{{M\begin{pmatrix}\sigma_{1} & 0 \\0 & \sigma_{2}\end{pmatrix}}M^{T}\mspace{14mu} {with}\mspace{14mu} {MM}^{T}} = {Id}}$

σ₁ and σ₂ are the principal components of F. We define the anisotropyfactor γ as:

${AF} = {\frac{{\max \left( {\sigma_{1},\sigma_{2}} \right)} - {\min \left( {\sigma_{1},\sigma_{2}} \right)}}{\min \left( {\sigma_{1},\sigma_{2}} \right)} \times 100}$

A suitable programming language, such as Python (version 2.7), can beused to generate the Fourier Transform image from the original image.The computer program can also be used to calculate the Anistropy Factor(AF).

FIG. 21A includes an image of a portion of a side surface of a particleformed according to an embodiment. FIG. 21B includes an image of theapplication of the Fourier Transform to the image of FIG. 21A. As can beseen, the surface of FIG. 21A includes ridges having a predominatedirection in the horizontal (i.e., left to right) direction. Such ridgesmay be the same as the microridges described in various embodimentsherein. The Fourier Transform analyzes these features and creates theimage of FIG. 21B, wherein a white cloud is presented that has moreintense values in the vertical direction (up and down) compared to thehorizontal direction. The PCA technique allows us to analyze andquantify the cloud depicted in FIG. 21B.

An abrasive particle of an embodiment herein may have a particular MAF,such as at least 1.25 or at least 1.30 or at least 1.40 or at least 1.50or at least 1.60 or at least 1.70 or at least 1.80 or at least 1.90 orat least 2.00 or at least 2.10 or at least 2.20 or at least 2.30 or atleast 2.40 or at least 2.50 or at least 2.60 or at least 2.70 or atleast 2.80 or at least 2.90 or at least 3.00 or at least 3.10 or atleast 3.20 or at least 3.30 or at least 3.40 or at least 3.50 or atleast 3.60 or at least 3.70. Still, according to one non-limitingembodiment, an abrasive particle may have a MAF of not greater than 20,such as not greater than 15 or not greater than 12 or not greater than10 or not greater than 8 or not greater than 7 or not greater than 6 ornot greater than 5 or not greater than 4. It will be appreciated thatthe MAF can be within a range including any of the minimum and maximumvalues noted above. Such values and ranges of values are relevant to acollection of abrasive particles formed according to an embodiment.

In another embodiment, the Anisotropy Factor (AF) described in theequations above can be plotted for one or more grains to create ahistogram of AF value versus frequency. From the histogram, one cancalculate an Anisotropy Factor Standard Deviation (i.e., first standarddeviation of the AF histogram). According to one embodiment, theAnisotropy Factor Standard Deviation can be at least 0.75, such as atleast 0.8 or at least 0.85 or at least 0.90 or at least 1.00 or at least1.05 or at least 1.10 or at least 1.20. Still, in another non-limitingembodiment, the Anisotropy Factor Standard Deviation can be not greaterthan 10, such as not greater than 9 or not greater than 8 or not greaterthan 7 or not greater than 6 or not greater than 5 or not greater than 4or not greater than 3 or not greater than 2. It will be appreciated thatthe Anisotropy Factor Standard Deviation can be within a range includingany of the minimum and maximum values noted above. Such values andranges of values are relevant to a collection of abrasive particlesformed according to an embodiment.

As noted herein, the MAF and Anisotropy Factor Standard Deviation can begenerated for a single abrasive particle or a collection of abrasiveparticles. To quantify MAF and Anisotropy Factor Standard Deviation fora single abrasive particle, a suitable number of regions of the sidesurface should be sampled (e.g., at least 3 distinct regions) togenerate a statistically relevant sample set. The MAF and AnisotropyFactor Standard Deviation should be measured at those regions thatappear to have the greatest texture (e.g., microridges) to the extentthat such regions are large enough for sampling. In some instances, suchregions may be associated with controlled cracking during processing. Aswill be described in embodiments herein the MAF and Anisotropy FactorStandard Deviation can also be used to analyze a collection of abrasiveparticles. To calculate these values based on a collection of abrasiveparticles, at least 8 abrasive particles are randomly selected from thecollection and three randomly selected regions of the side surface areanalyzed. To the extent that certain regions of the side surfacedemonstrate greater texture, such as illustrated in FIG. 21A, suchregions can be measured first presuming they are large enough foranalysis.

According to another aspect, certain abrasive particles of theembodiments herein can have distinct regions, which may have asignificantly different MAF and Anisotropy Factor Standard Deviationwith respect to each other. For example as illustrated in FIG. 19, theside surface 1804 can have first region 1805 and a second region 1806.The first region 1805 and second region 1806 can abut one another on theside surface 1804. The first region 1805 can extend from the first majorsurface 1802 and the second region 1806 can extend from the second majorsurface 1803. According to one embodiment, the second region can have aMAF that is greater than the MAF of the first region. As will beappreciated, such a comparison requires that the MAF analysis be doneseparately on each of the regions 1805 and 1806 and then compared toeach other. As noted in FIG. 19, the first region 1805 appears to have asmoother texture as compared to the second region 1806. The first region1805 may be associated with the patterning process. The second region1806 appears to have a rougher texture compared to the first region1806, which may be associated with one or more processing variablesincluding patterning leading to compression and/or controlled cracking.According to one embodiment, the difference in the MAF (i.e.,MAFΔ=MAF2/MAF1, wherein MAF2 is the MAF of second region 1806 and MAF1is the MAF of the first region 1805) between the first region 1805 andthe second region 1806 can be at least 1, such as at least 1.2 or atleast 1.4 or at least 1.6 or at least 1.8 or at least 2 or at least 2.2or at least 2.4 or at least 2.6 or at least 2.8 or at least 3 or atleast 3.5 or at least 4 or at least 5 or at least 6 or at least 7 or atleast 8. Still, in one non-limiting embodiment, the different in MAF canbe not greater than 1000 or not greater than 500 or not greater than 100or not greater than 50 or not greater than 10 or not greater than 5. Itwill be appreciated that the difference in MAF between the first region1805 and the second region 1806 can be within a range including any ofthe minimum and maximum values noted above. Such values and range ofvalues are relevant to a collection of abrasive particles according toembodiments herein.

According to one embodiment, the first region 1805 of an abrasiveparticle can have a particular MAF. For example, the MAF can be notgreater than 1.20, such as not greater than 1.10 or not greater than1.00 or not greater than 0.90 or not greater than 0.80 or not greaterthan 0.70 or not greater than 0.60 or not greater than 0.50 or notgreater than 0.40 or not greater than 0.30. Still, in one non-limitingembodiment, the MAF of the first region 1805 of an abrasive particle canbe at least 0.30 or at least 0.40 or at least 0.50 or at least 0.60 orat least 0.70 or at least 0.80 or at least 0.90 or at least 1.00 or atleast 1.10. It will be appreciated that the MAF of the first region 1805can be within a range including any of the minimum and maximum valuesnoted above. Such values and ranges of values are relevant to acollection of abrasive particles formed according to an embodiment.

In yet another aspect, the second region 1806 of an abrasive particlecan have a particular MAF, such as at least 1.30 or at least 1.40 or atleast 1.50 or at least 1.60 or at least 1.70 or at least 1.80 or atleast 1.90 or at least 2.00 or at least 2.10 or at least 2.20 or atleast 2.30 or at least 2.40 or at least 2.50 or at least 2.60 or atleast 2.70 or at least 2.80 or at least 2.90 or at least 3.00 or atleast 3.10 or at least 3.20 or at least 3.30 or at least 3.40 or atleast 3.50 or at least 3.60 or at least 3.70. In another non-limitingembodiment, the MAF of the second region 1806 of an abrasive particlecan be not greater than 20 or not greater than 15 or not greater than 12or not greater than 10 or not greater than 8 or not greater than 7 ornot greater than 6 or not greater than 5 or not greater than 4. It willbe appreciated that the MAF of the second region 1806 of an abrasiveparticle can be within a range including any of the minimum and maximumvalues noted above. Such values and ranges of values are relevant to acollection of abrasive particles formed according to an embodiment.

As noted above, FIG. 20 includes a side view image of an abrasiveparticle according to an embodiment including markings indicating therelative height of the body at three places and the relative height ofthe second region 1806 at the same three places. Abrasive particlesherein are described by a length, a width, and a height. The length isthe longest dimensions, the width is the second longest dimensionextending perpendicular to the length and within the same plane as thelength, and the height of the body is the shortest dimension extendingperpendicular to the length and perpendicular to the plane of the lengthand width. Identifying and measuring the length, width, and height ofshaped abrasive particles and constant height abrasive particles isstraightforward. Identifying and measuring the length, width, and heightof crushed or irregularly shaped abrasive particles is not as simple.Accordingly, to measure the height of irregularly shaped abrasiveparticles, a randomly selected sample of the abrasive particles isplaced on a surface and vibrated. The abrasive particles are presumed tohave aligned with their longest axis parallel to the surface and thusthe height is presumed to be the dimension extending perpendicular tothe surface and the length. After vibrating the abrasive particles toidentify the side surfaces, the abrasive particles are transferred to anadhesive surface using tweezers such that the side surface is visiblewhen viewed top-down. The grains are then prepared for imaging analysis(e.g., optical microscope, SEM, etc.)

As illustrated in FIG. 20, in certain instances, the second region 1806may have a particular average height relative to the average height ofthe body 1801 and relative to the average height of the first region1805. For example, in one embodiment the second region 1806 can extendfor a greater percentage of the height as compared to the first region1805. The average height of the body 1801 or any regions (e.g., firstand second regions 1805 and 1806) can be measured using an image asillustrated in FIG. 20 and an imaging processing software such asImageJ. A first line 1812 is drawn approximately in the middle of theside surface 1804 between the two exterior corners 1851 and 1852. Thefirst line 1811 is drawn to be approximately perpendicular to at leastone of the first and second major surfaces 1802 and 1803. A second line1811 is drawn to the left of the first line 1812 at a distanceapproximately midway between the first exterior corner 1851 and thefirst line 1812. A third line 1813 is drawn to the right of the firstline 1812 at a distance approximately midway between the second exteriorcorner 1852 and the first line 1812. The lengths of the lines 1811,1812, and 1813 are then averaged to define the average height of thebody 1801. The same process can be completed to measure the averageheight of the second region 1806 as illustrated by the lines 1821, 1822,and 1823.

According to one embodiment, the first region 1805 can have an averageheight of not greater than 90% of the height of the body 1801, such asnot greater than 80% or not greater than 70% or not greater than 60% ornot greater than 50% or not greater than 40% or not greater than 30% ornot greater than 20% or not greater than 10% or not greater than 5%.Still, in another embodiment, the first region 1805 can have an averageheight of at least 1% of the height of the body or at least 2% or atleast 5% or at least 8% or at least 10% or at least 15% or at least 20%or at least 30% or at least 40% or at least 50% or at least 60% or atleast 70% or at least 80%. It will be appreciated that the first region1805 can have an average height within a range including any of theminimum and maximum percentages noted above. In instances where the sidesurface clearly has only a first and second region (e.g., FIG. 20), theaverage height of the first region 1805 can be calculated by subtractingthe average height of the second region 1806 from the average height thebody 1801. Alternatively, one may measure the average height of thefirst region 1805 using the same process as described to measure theheight of the second region 1806, except taking care to measure onlythat portion relevant to the first region 1805.

In another embodiment, the second region 1806 can have an average heightof not greater than 90% of the height of the body 1801 or not greaterthan 80% or not greater than 70% or not greater than 60% or not greaterthan 50% or not greater than 40% or not greater than 30% or not greaterthan 20% or not greater than 10% or not greater than 5%. In stillanother non-limiting embodiment, the second region 1806 can have anaverage height of at least 5% of the height of the body or at least 8%or at least 9% or at least 10% or at least 12% or at least 15% or atleast 20% or at least 25% or at least 30% or at least 40% or at least50% or at least 60% or at least 70% or at least 80% or at least 90%. Itwill be appreciated that the second region 1806 can have an averageheight within a range including any of the minimum and maximumpercentages noted above. Such values and range of values are relevant toa collection of abrasive particles according to embodiments herein.

In certain instances, the abrasive particles of the embodiments hereincan have a particular shape on the side surface. As illustrated in FIGS.18 and 20, the sidewall 1804 can have a first region 1805 and a secondregion 1806 that can define a stepped region on the side surface of thebody 1801. That is, the second region 1806 can extend away from the bodyfurther than the first region 1805, defining a step surface 1831 thatmay have a least a portion extending substantially parallel to the firstmajor surface 1802 and/or the second major surface 1803.

As is evidence from the images provided in FIGS. 18-20, the secondregion 1806 of the side surface 1804 may have a texture that can be inthe form of a plurality of microridges as described in other embodimentsherein. In certain instances, the plurality of microridges can extend insubstantially the same direction relative to each other. It will beappreciated that any of the particles of any of the embodiments hereincan include one or more of a variety of features described in any of theembodiments herein.

As described in more detail herein, any one of the features described inthe embodiments herein can be associated with a collection of abrasiveparticles. Moreover, it will be appreciated that various combinations ofthe other features described in embodiments herein can be present in acollection of abrasive particles. A collection of abrasive particles canbe a plurality, and more particularly, a portion of abrasive particlespresent in a fixed abrasive article. The collection can be, but need notnecessarily be, formed according to an embodiment. The collection ofabrasive particles may in some circumstances include all particles thatare part of a fixed abrasive. Alternatively, a collection of abrasiveparticles may be a portion of free abrasive particles that are not partof a fixed abrasive article.

In one aspect, a collection of abrasive particles can include abrasiveparticles having a body including a first major surface, a second majorsurface opposite the first major surface, and a side surface extendingbetween the first major surface and the second major surface. Thecollection of abrasive particles may have a particular MeanNon-Convexity Factor (MNCF). The MNCF is used to describe thetwo-dimensional shape of the abrasive particles and is a mean valuegenerated from evaluating the non-convexity factor, which is calculatedfrom a two-dimensional, top-down image of the abrasive particles. Itshould be noted that a randomly selected abrasive particles are placedon a surface and vibrated. The abrasive particles are presumed to havealigned with their longest axis parallel to the surface and theparticles are imaged in such a position or transferred carefully to asuitable surface, being careful to maintain the orientation obtainedafter vibration, to be mounted for imaging.

As an example, FIGS. 22a, 22b and 22c include top-down images of thefirst major surface of an abrasive particle according to an embodiment.The image of FIG. 22A was obtained using X-ray microscopy, but one mayuse other suitable techniques to obtain a clear top-down image of theabrasive particles. After obtaining a suitable image as shown in FIG.22A, a binary image (i.e., only black and white) can be created bychoosing an appropriate threshold gray scale value that distinguishesblack and white and clearly delineate the edge of the particle from theback ground. Imaging software such as ImageJ may be used. The originalarea of the abrasive particle is calculated by the imaging softwareusing the binary image. Using the imaging software, a convex hull imageis created as shown in FIG. 22C. The convex hull defines the maximumarea of the two-dimensional image by identifying the exterior cornersand drawing straight lines between those corners. The convex hull areais measured using the image of FIG. 22C. The non-convexity factor (NCF)is then calculated according to the equation NCF=(1−(originalarea/convex hull area))×100. This process can be repeated for a suitablenumber of randomly sampled particles of the collection and then plottedas a histogram of non-convexity factor versus frequency. The MNCF can becalculated from the histogram by identifying the mean value.

According to one aspect, a collection of abrasive particles according toan embodiment can have a MNCF of at least 3.5, such as at least 3.75 orat least 4.0 or at least 4.5 or at least 5.0 or at least 5.5 or at least6.0 or at least 6.5 or at least 7.0 or at least 7.5 or at least 8.0 orat least 8.5 or at least 9.0. Still, in another non-limiting embodiment,the MNCF can be not greater than 30 or not greater than 25 or notgreater than 20 or not greater than 18 or not greater than 15 or notgreater than 14 or not greater than 13 or not greater than 12 or notgreater than 11 or not greater than 10.5. The MNCF can be within a rangeincluding any of the minimum and maximum values noted above. It shouldbe noted that the MNCF of the abrasive particles of the embodimentsherein may differ significantly from those of shaped abrasive particles,which are formed through different processes and typically have a higherdegree of shape fidelity and lower MNCF compared to each other.

Using the histogram of NCF versus frequency one may also evaluate theNon-Convexity Factor Standard Deviation (NCFSD) of the sampling ofabrasive particles from the collection of abrasive particles. The NCFSDis a first standard deviation measurement presuming a Gaussiandistribution of the data and may indicate the variation in thenon-convexity values. According to one embodiment, the abrasiveparticles of the collection can have a NCFSD of at least 2.4, such as atleast 2.5 or at least 2.6 or at least 2.7 or at least 2.8 or at least2.9 or at least 3.0 or at least 3.1 or at least 3.2 or at least 3.3 orat least 3.4 or at least 3.5. Still, in one non-limiting embodiment, theabrasive particles of the collection can have a NCFSD that is notgreater than 30, such as not greater than 25 or not greater than 20 ornot greater than 15 or not greater than 10 or not greater than 8 or notgreater than 6 or not greater than 4. The NCFSD can be within a rangeincluding any of the minimum and maximum values noted above.

The collection of abrasive particles can have any of the features notedin other embodiments, including for example, but not limited to MAF,Anisotropy Factor Standard Deviation, difference in MAF between a firstand second region of the side surface, average height of a first region,average height of a second region, difference in relative averageheights of the first and second regions to each other, the averageheight of the first region relative to the average height of the body,the average height of the second region relative to the average heightof the body or any combination thereof. The values of any of thefeatures of embodiments herein can be equally applicable to a collectionof abrasive particles, with the difference being that any features aremeasured from a suitable sampling of randomly selected abrasiveparticles as opposed to a single abrasive particle.

According to one embodiment, the collection of abrasive particles mayhave a particular standard deviation of height. The height is measuredas noted herein along the side surface in a direction substantiallyperpendicular to at least one of the first or second major surfaces. Theforming processes of the embodiments herein may facilitate formation ofabrasive particles having a controlled height and particular standarddeviation of height, such as not greater than 100 microns or not greaterthan 90 microns or not greater than 85 microns or not greater than 80microns or not greater than 75 microns or not greater than 70 microns ornot greater than 65 microns or not greater than 60 microns or notgreater than 55 microns or not greater than 50 microns or not greaterthan 45 microns or not greater than 40 microns or not greater than 35microns. Still, in one non-limiting embodiment, the abrasive particlesof the collection can have a standard deviation of height of at least 1micron, such as at least 5 microns or at least 10 microns or at least 15microns or at least 20 microns or at least 25 microns or at least 30microns or at least 35 microns. It will be appreciated that the standarddeviation of height for the collection of abrasive particles can bewithin a range including any of the minimum and maximum values notedabove.

FIG. 10 includes a cross-sectional illustration of a coated abrasivearticle incorporating the abrasive particulate material in accordancewith an embodiment. Notably, the plurality of abrasive particles on theone or more surfaces of the abrasive particles are not illustrated, butwill be appreciated as being present in accordance with embodimentsherein. As illustrated, the coated abrasive 1000 can include a substrate1001 and a make coat 1003 overlying a surface of the substrate 1001. Thecoated abrasive 1000 can further include a first type of abrasiveparticulate material 1005 in the form of a first type of abrasiveparticle (e.g., shaped, CHAP, unshaped or irregular, etc.), a secondtype of abrasive particulate material 1006 in the form of a second typeof abrasive particle (e.g., shaped, CHAP, unshaped or irregular, etc.),and a third type of abrasive particulate material in the form of diluentabrasive particles, which may have a random shape. The coated abrasive1000 may further include size coat 1004 overlying and bonded to theabrasive particulate materials 1005, 1006, 1007, and the make coat 1004.

According to one embodiment, the substrate 1001 can include an organicmaterial, inorganic material, and a combination thereof. In certaininstances, the substrate 1001 can include a woven material. However, thesubstrate 1001 may be made of a non-woven material. Particularlysuitable substrate materials can include organic materials, includingpolymers, and particularly, polyester, polyurethane, polypropylene,polyimides such as KAPTON from DuPont, paper. Some suitable inorganicmaterials can include metals, metal alloys, and particularly, foils ofcopper, aluminum, steel, and a combination thereof.

The make coat 1003 can be applied to the surface of the substrate 1001in a single process, or alternatively, the abrasive particulatematerials 1005, 1006, 1007 can be combined with a make coat 1003material and applied as a mixture to the surface of the substrate 1001.Suitable materials of the make coat 1003 can include organic materials,particularly polymeric materials, including for example, polyesters,epoxy resins, polyurethanes, polyamides, polyacrylates,polymethacrylates, poly vinyl chlorides, polyethylene, polysiloxane,silicones, cellulose acetates, nitrocellulose, natural rubber, starch,shellac, and mixtures thereof. In one embodiment, the make coat 1003 caninclude a polyester resin. The coated substrate can then be heated inorder to cure the resin and the abrasive particulate material to thesubstrate. In general, the coated substrate 1001 can be heated to atemperature of between about 100° C. to less than about 250° C. duringthis curing process.

Moreover, it will be appreciated that the coated abrasive article caninclude one or more collections of various types of abrasive particles,including the abrasive particulate materials 1005, 1006, and 1007, whichmay represent the abrasive particles of the embodiments herein. Theembodiments herein can include a fixed abrasive article (e.g., a coatedabrasive article) having a first collection of abrasive particles (e.g.,abrasive particulate materials 1005) representative of the abrasiveparticles of the embodiments herein. Any fixed abrasive may furtheremploy a second collection of abrasive particles therein, which may berepresentative of another type of abrasive particle according to theembodiments herein, which may be distinct in one or more manners fromthe abrasive particles of the first collection, including but notlimited to, one or more abrasive characteristics as described herein.The same features may be utilized in a bonded abrasive article.

The abrasive particulate materials 1005, 1006, and 1007 can includedifferent types of abrasive particles according to embodiments herein.The different types of abrasive particles can differ from each other incomposition, two-dimensional shape, three-dimensional shape, size, and acombination thereof as described in the embodiments herein. Asillustrated, the coated abrasive 1000 can include a first type ofabrasive particle 1005 and a second type of shaped abrasive particle1006. The coated abrasive 1000 can include different amounts of thefirst type and second type of abrasive particles 1005 and 1006. It willbe appreciated that the coated abrasive may not necessarily includedifferent types of abrasive particles, and can consist essentially of asingle type of abrasive particle. As will be appreciated, the abrasiveparticles of the embodiments herein can be incorporated into variousfixed abrasives (e.g., bonded abrasives, coated abrasive, non-wovenabrasives, thin wheels, cut-off wheels, reinforced abrasive articles,and the like), including in the form of blends, which may includedifferent types of shaped abrasive particles, shaped abrasive particleswith diluent particles, and the like. Moreover, according to certainembodiments, a batch of particulate material may be incorporated intothe fixed abrasive article in a predetermined orientation, wherein eachof the abrasive particles can have a predetermined orientation relativeto each other and relative to a portion of the abrasive article (e.g.,the backing of a coated abrasive).

The abrasive particles 1007 can be diluent particles different than thefirst and second types of abrasive particles 1005 and 1006. For example,the diluent particles can differ from the first and second types ofabrasive particles 1005 and 1006 in composition, two-dimensional shape,three-dimensional shape, size, and a combination thereof. For example,the abrasive particles 1007 can represent conventional, crushed abrasivegrit having random shapes. The abrasive particles 1007 may have a medianparticle size less than the median particle size of the first and secondtypes of abrasive particles 1005 and 1006.

After sufficiently forming the make coat 503 with the abrasiveparticulate materials 1005, 1006, 1007 contained therein, the size coat1004 can be formed to overlie and bond the abrasive particulatematerials 1005, 1006, 1007 in place. The size coat 1004 can include anorganic material, may be made essentially of a polymeric material, andnotably, can use polyesters, epoxy resins, polyurethanes, polyamides,polyacrylates, polymethacrylates, poly vinyl chlorides, polyethylene,polysiloxane, silicones, cellulose acetates, nitrocellulose, naturalrubber, starch, shellac, and mixtures thereof.

FIG. 11 includes an illustration of a bonded abrasive articleincorporating the abrasive particulate material in accordance with anembodiment. As illustrated, the bonded abrasive 1100 can include a bondmaterial 1101, abrasive particulate material 1102 contained in the bondmaterial, and porosity 1108 within the bond material 1101. In particularinstances, the bond material 1101 can include an organic material,inorganic material, and a combination thereof. Suitable organicmaterials can include polymers, such as epoxies, resins, thermosets,thermoplastics, polyimides, polyamides, and a combination thereof.Certain suitable inorganic materials can include metals, metal alloys,vitreous phase materials, crystalline phase materials, ceramics, and acombination thereof.

The abrasive particulate material 1102 of the bonded abrasive 1100 caninclude different types of abrasive particles 1103, 1104, 1105, and1106, which can have any of the features of different types of abrasiveparticles as described in the embodiments herein (e.g., shaped, CHAP,etc.). Notably, the different types of abrasive particles 1103, 1104,1105, and 1106 can differ from each other in composition,two-dimensional shape, three-dimensional shape, size, and a combinationthereof as described in the embodiments herein.

The bonded abrasive 1100 can include a type of abrasive particulatematerial 1107 representing diluent abrasive particles, which can differfrom the different types of abrasive particles 1103, 1104, 1105, and1106 in composition, two-dimensional shape, three-dimensional shape,size, and a combination thereof.

The porosity 1108 of the bonded abrasive 1100 can be open porosity,closed porosity, and a combination thereof. The porosity 1108 may bepresent in a majority amount (vol %) based on the total volume of thebody of the bonded abrasive 1100. Alternatively, the porosity 1108 canbe present in a minor amount (vol %) based on the total volume of thebody of the bonded abrasive 1100. The bond material 1101 may be presentin a majority amount (vol %) based on the total volume of the body ofthe bonded abrasive 1100. Alternatively, the bond material 1101 can bepresent in a minor amount (vol %) based on the total volume of the bodyof the bonded abrasive 1100. Additionally, abrasive particulate material1102 can be present in a majority amount (vol %) based on the totalvolume of the body of the bonded abrasive 1100. Alternatively, theabrasive particulate material 1102 can be present in a minor amount (vol%) based on the total volume of the body of the bonded abrasive 1100.

FIGS. 12A-12J include images of abrasive particles formed according tothe processes herein and define a collection of abrasive particles. Acollection of abrasive particles can include a group of particles thatare associated with a single abrasive article. In other instances, acollection of abrasive particles may include a plurality of particlesproduced in the same batch according to the same processing conditions.

According to one embodiment, a collection of abrasive particles caninclude at least a first abrasive particle and a second abrasiveparticle, wherein the first abrasive particle has a differenttwo-dimensional shape compared to the two-dimensional shape of thesecond abrasive particle. The two-dimensional shape is the shape of theparticle as viewed top-down in the plane defined by the length and widthof the particle body. For example, the particle of FIG. 12A has adifferent two-dimensional shape as compared to the two-dimensional shapeof the particle of FIG. 12B. Notably, the abrasive particles of FIGS.12A and 12B have irregular two-dimensional shapes characterized by sidesurface portions that have a combination of linear and arcuate shapes.The other abrasive particles of the collection, some of which areillustrated in FIGS. 12C-12J can also have the same distincttwo-dimensional shapes with respect to each other.

Moreover, as illustrated in FIGS. 12A-12J and according to oneembodiment, the abrasive particles of the collection can include anycombination of features of other abrasive particles described in theembodiments herein. For example, the abrasive particles of FIGS. 12A-12Jcan include one or more surface features (e.g., protrusions and/ordepressions), untextured regions, planar surfaces, linear or arcuateedges, or any combination thereof. Moreover, the arrangement of thesurface features between the particles within the collection of abrasiveparticles can vary. As illustrated in FIGS. 12A-12J, each of theparticles has a different arrangement of protrusions on the first majorsurface compared to the other particles of the collection.

The collection of abrasive particles can be incorporated into fixedabrasive, such as a coated abrasive, bonded abrasive, and the like.Within a collection there may be groups of particles. Groups ofparticles are particles that have the same two-dimensional shape withrespect to each other. For example, a collection of abrasive particlescan include a first group of abrasive particles, wherein each of theparticles of the first group has substantially the same two-dimensionalshape. Referring again to FIGS. 8A-8B and 9A-9E, each of the particlesin the illustrated images has a generally quadrilateral two-dimensionalshape and therefore can belong to the same group of abrasive particles.Particles of the same group may have, but need not necessarily have, thesame arrangement of surface features (e.g., protrusions, depressions,untextured regions, etc.). Suitable examples of the varioustwo-dimensional shapes include any of the two-dimensional shapes notedin the embodiments herein, including for example, but not limited to anirregular shape, a polygonal shape, a regular polygonal shape, anirregular polygonal shape, numerals, Greek alphabet characters, Latinalphabet characters, Russian alphabet characters, complex shapes havinga combination of polygonal shapes, a shape with linear and curvedportions, or any combination thereof.

It will be appreciated that the embodiments herein also include acollection of abrasive particles including at least one abrasiveparticle having a plurality of microridges along the side surface of thebody. Reference herein to the microridges will be understood to bereference to any type of the microridges or a combination of types ofmicroridges. More particularly, in one embodiment, a majority of theabrasive particles of the collection of abrasive particles can include aplurality of microridges on at least a portion of the side surfaces. Forexample, in at least one aspect, at least 51% of the abrasive particlesof the collection of abrasive particles include the plurality ofmicroridges on at least a portion of their side surface, such as atleast 52% or at least 54% or at least 56% or at least 58% or at least60% or at least 62% or at least 64% or at least 66% or at least 68% orat least 70% or at least 72% or at least 74% or at least 76% or at least78% or at least 80% or at least 82% or at least 84% or at least 86% orat least 88% or at least 90% or at least 92% or at least 94% or at least96% or at least 98% or at least 99% of the abrasive particles of thecollection of abrasive particles. Still, in at least one non-limitingembodiment, not greater than 99% of the abrasive particles of thecollection of abrasive particles may include the plurality ofmicroridges on at least a portion of the side surface, such as, notgreater than 98% or not greater than 96% or not greater than 94% or notgreater than 92% or not greater than 90% or not greater than 88% or notgreater than 86% or not greater than 84% or not greater than 82% or notgreater than 80% or not greater than 78% or not greater than 76% or notgreater than 74% or not greater than 72% or not greater than 70% or notgreater than 68% or not greater than 66% or not greater than 64% or notgreater than 62% or not greater than 60% or not greater than 58% or notgreater than 56% or not greater than 54% or not greater than 52% of theabrasive particles of the collection of abrasive particles. It will beappreciated that the percentage of abrasive particles in the collectionof abrasive particles including the plurality of microridges on at leasta portion of the side surfaces can be within a range including any ofthe minimum and maximum percentages noted above.

In yet another embodiment, a majority of the total surface area of theside surfaces of the abrasive particles in the collection can include aplurality of microridges. For example, at least 51% of the total surfacearea of the side surfaces of the abrasive particles of the collectioncan include the plurality of microridges or at least 52% or at least 54%or at least 56% or at least 58% or at least 60% or at least 62% or atleast 64% or at least 66% or at least 68% or at least 70% or at least72% or at least 74% or at least 76% or at least 78% or at least 80% orat least 82% or at least 84% or at least 86% or at least 88% or at least90% or at least 92% or at least 94% or at least 96% or at least 98% orat least 99%. In one non-limiting embodiment, not greater than 99% ofthe total surface area of the sides surfaces of the abrasive particlesof the collection can include the plurality of microridges, such as, notgreater than 98% or not greater than 96% or not greater than 94% or notgreater than 92% or not greater than 90% or not greater than 88% or notgreater than 86% or not greater than 84% or not greater than 82% or notgreater than 80% or not greater than 78% or not greater than 76% or notgreater than 74% or not greater than 72% or not greater than 70% or notgreater than 68% or not greater than 66% or not greater than 64% or notgreater than 62% or not greater than 60% or not greater than 58% or notgreater than 56% or not greater than 54% or not greater than 52%. Itwill be appreciated that the total surface area of the side surface ofthe abrasive particles in the collection including the plurality ofmicroridges can be within a range including any of the minimum andmaximum percentages noted above.

In yet another aspect, the side surfaces of the bodies of the abrasiveparticles having side surface portions, where each side surface portionis that portion of the side surface extending between external cornersof the body. Generally, each abrasive particle has at least three sidesurface portions extending around the peripheral surface of the bodybetween the first and second major surfaces. For at least oneembodiment, the collection of abrasive particles can be formed such thatat least one abrasive particle in the collection has at least 45% of theside surface portions of the body including the plurality ofmicroridges. In another embodiment, at least 10% of the abrasiveparticles of the collection have at least 45% of the side surfaceportion of the body including the plurality of microridges. In otherinstances, the percentage of abrasive particles in the collection havingat least 45% of the side surface portions of the body including theplurality of microridges can be greater, such as at least 20% or atleast 30% or at least 40% or at least 50% or at least 60% or at least70% or at least 80% or at least 90% or at least 95% It will beappreciated that in one embodiment, each of the abrasive particles ofthe collection can include at least 45% of the side surface portions ofthe body including the plurality of microridges. Still, in onenon-limiting embodiment, the percentage of abrasive particles of thecollection including at least 45% of the side surface portions of thebody including the plurality of microridges can be not greater than 98%or not greater than 90% or not greater than 80% or not greater than 70%or not greater than 60% or not greater than 50% or not greater than 40%or not greater than 30% or not greater than 20% or not greater than 10%.It will be appreciated that the percentage of abrasive particles of thecollection having at least 45% of the side surface portions of the bodyincluding the plurality of microridges can be within a range includingany of the minimum and maximum values noted above.

In still another embodiment, the collection of abrasive particles caninclude abrasive particles having a greater percentage of the sidesurface portions including the plurality of microridges. For example, atleast 52% of the side surface portions of the body include the pluralityof microridges, or at least 54% or at least 56% or at least 58% or atleast 60% or at least 62% or at least 64% or at least 66% or at least68% or at least 70% or at least 72% or at least 74% or at least 76% orat least 78% or at least 80% or at least 82% or at least 84% or at least86% or at least 88% or at least 90% or at least 92% or at least 94% orat least 96% or at least 98% or at least 99% of the side surfaceportions of the body include the plurality of microridges. It will beappreciated that the percentage of side surface portions including theplurality of microridges can be combined with any of the foregoingpercentages of particle in the collection identified as having theplurality of microridges. For example, it is contemplated that incertain embodiments, at least 10% of the abrasive particles of thecollection can have at least 50% of their side surface portions havingthe plurality of microridges. In another example, at least 50% of theabrasive particles of the collection may have at least 50% of their sidesurface portions having the plurality of microridges. And as a furtherexample, in another embodiment, it may be noted that at least 70% of theabrasive particles of the collection may have at least 60% of their sidesurface portions having the plurality of microridges. And yet in anotherembodiment, each of the abrasive particles of the collection can haveall side surface portions including the plurality of microridges.

The formation of a collection of abrasive particles, which may or maynot have discrete groups of abrasive particles in the collection may becontrolled by one or more process parameters, including but not limitedto, the shape of the form used to modify the mixture, the modificationprocess, the drying process, and the like. It will be appreciated that acollection of abrasive particle can include a plurality of groups ofabrasive particles, and particularly, more than two distinct groups ofabrasive particles.

Many different aspects and embodiments are possible. Some of thoseaspects and embodiments are described herein. After reading thisspecification, skilled artisans will appreciate that those aspects andembodiments are only illustrative and do not limit the scope of thepresent invention. Embodiments may be in accordance with any one or moreof the embodiments as listed below.

EMBODIMENTS

Embodiment 1. An abrasive particle comprising:

a body including a first major surface, a second major surface oppositethe first major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein the side surfacecomprises a Mean Anisotropy Factor of at least 1.25.

Embodiment 2. An abrasive particle comprising:

a body including a first major surface, a second major surface oppositethe first major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein the first majorsurface comprises a first protrusion disposed abutting a first sidesurface portion and extending along at least a portion of the first sidesurface portion, and further comprising an untextured region extendingthrough a central region of the body, wherein the untextured regiondefines a majority of a total surface area of the first major surface.

Embodiment 3. An abrasive particle comprising:

a body including a first major surface, a second major surface oppositethe first major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein a majority of theside surface comprises a plurality of microridges.

Embodiment 4. The abrasive particle of any one of embodiments 2 and 3,wherein the side surface comprises a Mean Anisotropy Factor of at least1.25.

Embodiment 5. The abrasive particle of any one of embodiments 1 and 4,wherein the Mean Anisotropy Factor is at least 1.30 or at least 1.40 orat least 1.50 or at least 1.60 or at least 1.70 or at least 1.80 or atleast 1.90 or at least 2.00 or at least 2.10 or at least 2.20 or atleast 2.30 or at least 2.40 or at least 2.50 or at least 2.60 or atleast 2.70 or at least 2.80 or at least 2.90 or at least 3.00 or atleast 3.10 or at least 3.20 or at least 3.30 or at least 3.40 or atleast 3.50 or at least 3.60 or at least 3.70.

Embodiment 6. The abrasive particle of any one of embodiments 1 and 4,wherein the Mean Anisotropy Factor is not greater than 20 or not greaterthan 15 or not greater than 12 or not greater than 10 or not greaterthan 8 or not greater than 7 or not greater than 6 or not greater than 5or not greater than 4.

Embodiment 7. The abrasive particle of any one of embodiments 1, 2, and3, wherein the side surface comprises an Anisotropy Factor StandardDeviation of at least 0.75 or at least 0.8 or at least 0.85 or at least0.90 or at least 1.00 or at least 1.05 or at least 1.10 or at least1.20.

Embodiment 8. The abrasive particle of any one of embodiments 1, 2, and3, wherein the side surface comprises an Anisotropy Factor StandardDeviation of not greater than 10 or not greater than 9 or not greaterthan 8 or not greater than 7 or not greater than 6 or not greater than 5or not greater than 4 or not greater than 3 or not greater than 2.

Embodiment 9. The abrasive particle of any one of embodiments 1, 2, and3, wherein the side surface comprises a first region extending from thefirst major surface and a second region extending from the second majorsurface, and wherein the first region and second region abut on the sidesurface, and wherein the second region comprises a Mean AnisotropyFactor that is greater than the first region.

Embodiment 10. The abrasive particle of embodiment 9, wherein the secondregion extends for a greater percentage of the height as compared to thefirst region.

Embodiment 11. The abrasive particle of embodiment 9, wherein the firstregion has an average height of not greater than 90% of the height ofthe body or not greater than 80% or not greater than 70% or not greaterthan 60% or not greater than 50% or not greater than 40% or not greaterthan 30% or not greater than 20% or not greater than 10% or not greaterthan 5%.

Embodiment 12. The abrasive particle of embodiment 9, wherein the firstregion has an average height of at least 1% of the height of the body orat least 2% or at least 5% or at least 8% or at least 10% or at least15% or at least 20% or at least 30% or at least 40% or at least 50% orat least 60% or at least 70% or at least 80%.

Embodiment 13. The abrasive particle of embodiment 9, wherein the secondregion comprises an average height of not greater than 90% of the heightof the body or not greater than 80% or not greater than 70% or notgreater than 60% or not greater than 50% or not greater than 40% or notgreater than 30% or not greater than 20% or not greater than 10% or notgreater than 5%.

Embodiment 14. The abrasive particle of embodiment 9, wherein the secondregion has an average height of at least 5% of the height of the body orat least 8% or at least 9% or at least 10% or at least 12% or at least15% or at least 20% or at least 25% or at least 30% or at least 40% orat least 50% or at least 60% or at least 70% or at least 80% or at least90%.

Embodiment 15. The abrasive particle of embodiment 9, wherein the firstregion comprises a Mean Anisotropy Factor of not greater than 1.20 ornot greater than 1.10 or not greater than 1.00 or not greater than 0.90or not greater than 0.80 or not greater than 0.70 or not greater than0.60 or not greater than 0.50 or not greater than 0.40 or not greaterthan 0.30.

Embodiment 16. The abrasive particle of embodiment 9, wherein the MeanAnisotropy Factor of the first region is at least 0.30 or at least 0.40or at least 0.50 or at least 0.60 or at least 0.70 or at least 0.80 orat least 0.90 or at least 1.00 or at least 1.10.

Embodiment 17. The abrasive particle of embodiment 9, wherein the MeanAnisotropy Factor of the second region at least 1.30 or at least 1.40 orat least 1.50 or at least 1.60 or at least 1.70 or at least 1.80 or atleast 1.90 or at least 2.00 or at least 2.10 or at least 2.20 or atleast 2.30 or at least 2.40 or at least 2.50 or at least 2.60 or atleast 2.70 or at least 2.80 or at least 2.90 or at least 3.00 or atleast 3.10 or at least 3.20 or at least 3.30 or at least 3.40 or atleast 3.50 or at least 3.60 or at least 3.70.

Embodiment 18. The abrasive particle of embodiment 9, wherein the MeanAnisotropy Factor of the second region is not greater than 20 or notgreater than 15 or not greater than 12 or not greater than 10 or notgreater than 8 or not greater than 7 or not greater than 6 or notgreater than 5 or not greater than 4.

Embodiment 19. The abrasive particle of embodiment 9, wherein the firstregion and second region define a stepped region on the side surface ofthe body.

Embodiment 20. The abrasive particle of embodiment 9, wherein the secondregion comprises a plurality of microridges.

Embodiment 21. The abrasive particle of embodiment 20, wherein theplurality of microridges extend in substantially the same directionrelative to each other.

Embodiment 22. The abrasive particle of any one of embodiments 1, 2, and3, wherein the first major surface and second major surface aresubstantially parallel to each other.

Embodiment 23. The abrasive particle of any one of embodiments 1 and 2,wherein a majority of the side surface comprises a plurality ofmicroridges.

Embodiment 24. The abrasive particle of any one of embodiments 3 and 23,wherein at least a portion of the plurality of microridges comprises aplurality of isolated microridges defined by microridges extending fromthe side surface and separated by generally smooth planar regions.

Embodiment 25. The abrasive particle of embodiment 24, wherein theplurality of isolated microridges extend along the side surface in anirregular path.

Embodiment 26. The abrasive particle of embodiment 24, wherein at leastone of the isolated microridges of the plurality of isolated microridgescomprises a head region and a tail region connected to and extendingfrom the head region, wherein the head region has a rounded shape andthe tail region has an elongated shape.

Embodiment 27. The abrasive particle of any one of embodiments 3 and 23,wherein at least a portion of the plurality of microridges comprises aplurality of scaled microridges.

Embodiment 28. The abrasive particle of embodiment 27, wherein at leasta portion of the scaled microridges of the plurality of scaledmicroridges comprise a primary ridge and a plurality of wrinklesextending from the primary ridge.

Embodiment 29. The abrasive particle of embodiment 28, wherein theprimary ridge extends along the side surface in an irregular path.

Embodiment 30. The abrasive particle of embodiment 28, wherein at leasta portion of the plurality of wrinkles extend along the side surface inan irregular path away from the primary ridge.

Embodiment 31. The abrasive particle of embodiment 28, wherein thewrinkles are defined grooves extending along the side surface along anirregular path.

Embodiment 32. The abrasive particle of embodiment 28, wherein thewrinkles extend along a curved path.

Embodiment 33. The abrasive particle of embodiment 28, wherein theplurality of scaled microridges includes a greater number of wrinklescompared to the number of primary ridges.

Embodiment 34. The abrasive particle of embodiment 28, wherein thewrinkles extend in a different direction compared to one or more primaryridges, and the wrinkles extend between two or more primary ridges.

Embodiment 35. The abrasive particle of embodiment 28, wherein theprimary ridge includes at least one gap between elongated portions.

Embodiment 36. The abrasive particle of embodiment 27, wherein at leasta portion of the scaled microridges have a scaled appearance.

Embodiment 37. The abrasive particle of embodiment 27, wherein at leasta portion of the scaled microridges have a layered appearance.

Embodiment 38. The abrasive particle of embodiment 27, wherein at leasta portion of the scaled microridges include a plurality of raisedportions with irregular shapes and wrinkles extending between theplurality of raised portions.

Embodiment 39. The abrasive particle of any one of embodiments 3 and 23,wherein the plurality of microridges is a conchoidal fracturing feature.

Embodiment 40. The abrasive particle of any one of embodiments 3 and 23,wherein the plurality of microridges is formed during controlledcracking of the side surface.

Embodiment 41. The abrasive particle of any one of embodiments 3 and 23,wherein the plurality of microridges includes a precipice region.

Embodiment 42. The abrasive particle of any one of embodiments 3 and 23,wherein at least 51% of the total surface area of the side surfaceincludes the plurality of microridges or at least 52% or at least 54% orat least 56% or at least 58% or at least 60% or at least 62% or at least64% or at least 66% or at least 68% or at least 70% or at least 72% orat least 74% or at least 76% or at least 78% or at least 80% or at least82% or at least 84% or at least 86% or at least 88% or at least 90% orat least 92% or at least 94% or at least 96% or at least 98% or at least99%.

Embodiment 43. The abrasive particle of embodiment 42, wherein notgreater than 99% of the total surface area of the sides surface includesthe plurality of microridges or not greater than 98% or not greater than96% or not greater than 94% or not greater than 92% or not greater than90% or not greater than 88% or not greater than 86% or not greater than84% or not greater than 82% or not greater than 80% or not greater than78% or not greater than 76% or not greater than 74% or not greater than72% or not greater than 70% or not greater than 68% or not greater than66% or not greater than 64% or not greater than 62% or not greater than60% or not greater than 58% or not greater than 56% or not greater than54% or not greater than 52%.

Embodiment 44. The abrasive particle of any one of embodiments 3 and 23,wherein the side surface of the body includes side surface portions, andwherein each side surface portion extends between external corners ofthe body, and wherein at least 45% of the side surface portions includethe plurality of microridges.

Embodiment 45. The abrasive particle of embodiment 44, wherein the bodyincludes at least three side surface portions including the plurality ofmicroridges.

Embodiment 46. The abrasive particle of embodiment 44, wherein all ofthe side surface portions include the plurality of microridges.

Embodiment 47. The abrasive particle of embodiment 44, wherein at least52% of the side surface portions of the body include the plurality ofmicroridges, or at least 54% or at least 56% or at least 58% or at least60% or at least 62% or at least 64% or at least 66% or at least 68% orat least 70% or at least 72% or at least 74% or at least 76% or at least78% or at least 80% or at least 82% or at least 84% or at least 86% orat least 88% or at least 90% or at least 92% or at least 94% or at least96% or at least 98% or at least 99%.

Embodiment 48. The abrasive particle of embodiment 44, wherein the bodyincludes at least one side surface portion that does not include theplurality of microridges.

Embodiment 49. The abrasive particle of any one of embodiments 1 and 3,further comprising a first protrusion abutting the first side surfaceportion and extending along at least a portion of the first side surfaceportion.

Embodiment 50. The abrasive particle of any one of embodiments 2 and 49,wherein the first major surface comprises a first depression extendingin a direction parallel to a first side surface portion, and wherein thefirst protrusion is disposed between the first side surface portion andthe first depression, the first protrusion abutting the first sidesurface portion and extending along at least a portion of the first sidesurface portion.

Embodiment 51. The abrasive particle of any one of embodiments 2 and 50,wherein the first protrusion extends for at least 30% of the totallength of the first side surface portion or at least 40% of the totallength of the first side surface portion or at least 50% of the totallength of the first side surface portion or at least 60% of the totallength of the first side surface portion or at least 70% of the totallength of the first side surface portion or at least 80% of the totallength of the first side surface portion or at least 90% of the totallength of the first side surface portion.

Embodiment 52. The abrasive particle of any one of embodiments 2 and 50,wherein the first depression extends for at least 30% of the totallength of the first side surface portion or at least 40% of the totallength of the first side surface portion or at least 50% of the totallength of the first side surface portion or at least 60% of the totallength of the first side surface portion or at least 70% of the totallength of the first side surface portion or at least 80% of the totallength of the first side surface portion or at least 90% of the totallength of the first side surface portion.

Embodiment 53. The abrasive particle of any one of embodiments 2 and 50,wherein the first side surface portion is defined as a portion of theside surface extending between two external corners of the body.

Embodiment 54. The abrasive particle of any one of embodiments 2 and 50,wherein the first side surface portion is a fraction of the total lengthof the side surface defining the perimeter of the body.

Embodiment 55. The abrasive particle of any one of embodiments 2 and 50,wherein the first protrusion extends for a fraction of the total lengthof the side surface defining the perimeter of the body.

Embodiment 56. The abrasive particle of any one of embodiments 2 and 50,wherein the first depression extends for a fraction of the total lengthof the side surface defining the perimeter of the body.

Embodiment 57. The abrasive particle of any one of embodiments 2 and 50,wherein the first side surface portion and first protrusion havesubstantially the same contour as viewed in the plane of the first majorsurface.

Embodiment 58. The abrasive particle of any one of embodiments 2 and 50,wherein the first protrusion intersects a second side surface portionthat is distinct from the first side surface portion.

Embodiment 59. The abrasive particle of any one of embodiments 1 and 3,further comprising an untextured region extending through a centralregion of the body, wherein the untextured region defines a majority ofa total surface area of the first major surface.

Embodiment 60. The abrasive particle of any one of embodiments 2 and 59,wherein the untextured region defines at least 55% of the total surfacearea of the first major surface or at least 60% or at least 65% or atleast 70% or at least 75% or at least 80% or at least 85% or at least90%.

Embodiment 61. The abrasive particle of any one of embodiments 2 and 59,wherein the untextured region defines not greater than 99% of the totalsurface area of the first major surface or not greater than 95% or notgreater than 90% or not greater than 85% or not greater than 80% or notgreater than 75% or not greater than 70% or not greater than 65% or notgreater than 60% or not greater than 55%.

Embodiment 62. The abrasive particle of any one of embodiments 2 and 59,wherein the first protrusion abuts a portion of the untextured region,and wherein the first protrusion is spaced apart from the central regionof the body.

Embodiment 63. The abrasive particle of any one of embodiments 2 and 59,wherein the first protrusion extends above the surface of the untexturedregion.

Embodiment 64. The abrasive particle of any one of embodiments 2 and 59,wherein the untextured region abuts a portion of the side surface of thebody.

Embodiment 65. The abrasive particle of any one of embodiments 2 and 59,wherein the untextured region comprises a two-dimensional shapesubstantially the same as the two-dimensional shape of the body.

Embodiment 66. The abrasive particle of any one of embodiments 2 and 50,wherein the first depression has an average depth that is at least 5%and not greater than 99% of an average height of the body.

Embodiment 67. The abrasive particle of any one of embodiments 2 and 50,wherein the first protrusion has an average height that is at least 5%and not greater than 99% of an average height of the body.

Embodiment 68. The abrasive particle of any one of embodiments 2 and 50,further comprising a second protrusion abutting a second side surfaceportion and extending along the second side surface portion.

Embodiment 69. The abrasive particle of embodiment 68, wherein the firstmajor surface comprises a second depression extending in a directionparallel to the second side surface portion.

Embodiment 70. The abrasive particle of embodiment 69, wherein the firstdepression intersects the second depression.

Embodiment 71. The abrasive particle of embodiment 69, wherein the firstdepression and second depression intersect proximate to an externalcorner separating the first side surface portion and second side surfaceportion.

Embodiment 72. The abrasive particle of embodiment 69, wherein thesecond protrusion abuts the first depression.

Embodiment 73. The abrasive particle of embodiment 69, wherein the firstprotrusion abuts the second depression.

Embodiment 74. The abrasive particle of embodiment 69, wherein the firstprotrusion abuts the second protrusion.

Embodiment 75. The abrasive particle of any one of embodiments 2 and 50,further comprising an unfeatured edge extending between the first majorsurface and a third portion of a side surface, wherein the third sidesurface portion is distinct from the first side surface portion.

Embodiment 76. The abrasive particle of embodiment 75, wherein the thirdside surface portion and first side surface portion are separated fromeach other by at least one external corner on the side surface.

Embodiment 77. The abrasive particle of any one of embodiments 2 and 50,wherein the body includes a bottom edge joining the second major surfaceand the side surface, wherein at least a portion of the bottom edge hasan irregular contour.

Embodiment 78. The abrasive particle of any one of embodiments 1, 2 and3, wherein the body comprises a two-dimensional shape as viewed in aplane defined by a length and a width of the body selected from thefirst group consisting of regular polygons, irregular polygons,ellipsoids, numerals, Greek alphabet characters, Latin alphabetcharacters, Russian alphabet characters, complex shapes having acombination of polygonal shapes, a shape with linear and curvedportions, and a combination thereof.

Embodiment 79. The abrasive particle of any one of embodiments 1, 2 and3, wherein the body comprises an irregular two-dimensional shape asviewed in a plane defined by a length and a width of the body.

Embodiment 80. The abrasive particle of any one of embodiments 1, 2 and3, wherein the body includes at least one material from the group ofoxides, carbides, nitrides, borides, oxycarbides, oxynitrides,oxyborides, natural minerals, synthetic materials, carbon-basedmaterials, and a combination thereof.

Embodiment 81. The abrasive particle of any one of embodiments 1, 2 and3, wherein the body comprises alumina.

Embodiment 82. The abrasive particle of any one of embodiments 1, 2 and3, wherein the body consists essentially of alumina.

Embodiment 83. The abrasive particle of any one of embodiments 1, 2 and3, wherein the body includes at least one oxide from the group ofaluminum oxide, zirconium oxide, titanium oxide, yttrium oxide, chromiumoxide, strontium oxide, silicon oxide, magnesium oxide, rare-earthoxides, or any combination thereof.

Embodiment 84. The abrasive particle of any one of embodiments 1, 2 and3, further comprising a fixed abrasive including the abrasive particle.

Embodiment 85. The abrasive particle of embodiment 69, wherein the fixedabrasive is a coated abrasive.

Embodiment 86. The abrasive particle of embodiment 69, wherein the fixedabrasive is a bonded abrasive.

Embodiment 87. A collection of abrasive particles comprising:

a first abrasive particle comprising:a body including a first major surface, a second major surface oppositethe first major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein the body of thefirst abrasive particle comprises a first two-dimensional shape, andwherein the first major surface comprises a first protrusion abuttingand extending along at least a portion of a first side surface portionof the side surface, and wherein the body further comprises anuntextured region extending through a central region of the body,wherein the untextured region defines a majority of a total surface areaof the first major surface; and a second abrasive particle comprising:a body including a first major surface, a second major surface oppositethe first major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein the body of thesecond abrasive particle comprises a two-dimensional shape that isdifferent compared to the two-dimensional shape of the first abrasiveparticle.

Embodiment 88. A collection of abrasive particles, wherein each abrasiveparticle of the collection of abrasive particles includes a body havinga first major surface, a second major surface opposite the first majorsurface, and a side surface extending between the first major surfaceand the second major surface, and wherein a majority of the particles ofthe collection of abrasive particles comprises a plurality ofmicroridges extending along at least a portion of the sides surface.

Embodiment 89. A collection of abrasive particles, wherein an abrasiveparticle of the collection of abrasive particles includes:

a body having a first major surface, a second major surface opposite thefirst major surface, and a side surface extending between the firstmajor surface and the second major surface, and wherein the side surfaceincludes a plurality of side surface portions extending between externalcorners of the body; and wherein at least 45% of the side surfaceportions of the body include a plurality of microridges.

Embodiment 90. A collection of abrasive particles, wherein each abrasiveparticle of the collection of abrasive particles comprises:

a body having a first major surface, a second major surface opposite thefirst major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein the first majorsurface and second major surface are substantially parallel with eachother; and wherein the collection of abrasive particles comprises a MeanNon-Convexity Factor of at least 3.5 and a Non-Convexity Factor StandardDeviation of at least 2.4.

Embodiment 91. A collection of abrasive particles, wherein each abrasiveparticle of the collection of abrasive particles comprises:

a body having a first major surface, a second major surface opposite thefirst major surface, and a side surface extending between the firstmajor surface and the second major surface; and wherein the collectionof abrasive particles comprises a Mean Anisotropy Factor of at least1.25.

Embodiment 92. A collection of abrasive particles, wherein each abrasiveparticle of the collection of abrasive particles comprises:

a body having a first major surface, a second major surface opposite thefirst major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein the body comprises aheight as defined as the distance along the side surface between thefirst major surface and the second major surface;wherein the collection of abrasive particles comprises a standarddeviation of height of not greater than 100; and wherein the collectionof abrasive particles comprises a Mean Non-Convexity Factor of at least3.5.

Embodiment 93. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, and 92, further comprising a Mean AnisotropyFactor of at least 1.25.

Embodiment 94. The collection of abrasive particles of any one ofembodiments 91 and 93, wherein the Mean Anisotropy Factor is at least1.30 or at least 1.40 or at least 1.50 or at least 1.60 or at least 1.70or at least 1.80 or at least 1.90 or at least 2.00 or at least 2.10 orat least 2.20 or at least 2.30 or at least 2.40 or at least 2.50 or atleast 2.60 or at least 2.70 or at least 2.80 or at least 2.90 or atleast 3.00 or at least 3.10 or at least 3.20 or at least 3.30 or atleast 3.40 or at least 3.50 or at least 3.60 or at least 3.70.

Embodiment 95. The collection of abrasive particles of any one ofembodiments 91 and 93, wherein the Mean Anisotropy Factor is not greaterthan 20 or not greater than 15 or not greater than 12 or not greaterthan 10 or not greater than 8 or not greater than 7 or not greater than6 or not greater than 5 or not greater than 4.

Embodiment 96. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, further comprising an AnisotropyFactor Standard Deviation of at least 0.75 or at least 0.8 or at least0.85 or at least 0.90 or at least 1.00 or at least 1.05 or at least 1.10or at least 1.20.

Embodiment 97. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, further an Anisotropy FactorStandard Deviation of not greater than 10 or not greater than 9 or notgreater than 8 or not greater than 7 or not greater than 6 or notgreater than 5 or not greater than 4 or not greater than 3 or notgreater than 2.

Embodiment 98. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, wherein the side surfacecomprises a first region extending from the first major surface and asecond region extending from the second major surface, and wherein thefirst region and second region abut on the side surface, and wherein thesecond region comprises a Mean Anisotropy Factor that is greater thanthe first region.

Embodiment 99. The collection of abrasive particles of embodiment 98,wherein the second region extends for a greater percentage of the heightas compared to the first region.

Embodiment 100. The collection of abrasive particles of embodiment 98,wherein the first region has an average height of not greater than 90%of the height of the body or not greater than 80% or not greater than70% or not greater than 60% or not greater than 50% or not greater than40% or not greater than 30% or not greater than 20% or not greater than10% or not greater than 5%.

Embodiment 101. The collection of abrasive particles of embodiment 98,wherein the first region has an average height of at least 1% of theheight of the body or at least 2% or at least 5% or at least 8% or atleast 10% or at least 15% or at least 20% or at least 30% or at least40% or at least 50% or at least 60% or at least 70% or at least 80%.

Embodiment 102. The collection of abrasive particles of embodiment 98,wherein the second region comprises an average height of not greaterthan 90% of the height of the body or not greater than 80% or notgreater than 70% or not greater than 60% or not greater than 50% or notgreater than 40% or not greater than 30% or not greater than 20% or notgreater than 10% or not greater than 5%.

Embodiment 103. The collection of abrasive particles of embodiment 98,wherein the first region has an average height of at least 5% of theheight of the body or at least 8% or at least 9% or at least 10% or atleast 12% or at least 15% or at least 20% or at least 25% or at least30% or at least 40% or at least 50% or at least 60% or at least 70% orat least 80% or at least 90%.

Embodiment 104. The collection of abrasive particles of embodiment 98,wherein the first region comprises a Mean Anisotropy Factor of notgreater than 1.20 or not greater than 1.10 or not greater than 1.00 ornot greater than 0.90 or not greater than 0.80 or not greater than 0.70or not greater than 0.60 or not greater than 0.50 or not greater than0.40 or not greater than 0.30.

Embodiment 105. The collection of abrasive particles of embodiment 98,wherein the Mean Anisotropy Factor of the first region is at least 0.30or at least 0.40 or at least 0.50 or at least 0.60 or at least 0.70 orat least 0.80 or at least 0.90 or at least 1.00 or at least 1.10.

Embodiment 106. The collection of abrasive particles of embodiment 98,wherein the Mean Anisotropy Factor of the second region at least 1.30 orat least 1.40 or at least 1.50 or at least 1.60 or at least 1.70 or atleast 1.80 or at least 1.90 or at least 2.00 or at least 2.10 or atleast 2.20 or at least 2.30 or at least 2.40 or at least 2.50 or atleast 2.60 or at least 2.70 or at least 2.80 or at least 2.90 or atleast 3.00 or at least 3.10 or at least 3.20 or at least 3.30 or atleast 3.40 or at least 3.50 or at least 3.60 or at least 3.70.

Embodiment 107. The collection of abrasive particles of embodiment 98,wherein the Mean Anisotropy Factor of the second region is not greaterthan 20 or not greater than 15 or not greater than 12 or not greaterthan 10 or not greater than 8 or not greater than 7 or not greater than6 or not greater than 5 or not greater than 4.

Embodiment 108. The collection of abrasive particles of embodiment 98,wherein the first region and second region define a stepped region onthe side surface of the body.

Embodiment 109. The collection of abrasive particles of embodiment 98,wherein the second region comprises a plurality of microridges.

Embodiment 110. The collection of abrasive particles of embodiment 98,wherein the plurality of microridges extend in substantially the samedirection relative to each other.

Embodiment 111. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 91, and 92, further comprising a MeanNon-Convexity Factor of at least 3.5.

Embodiment 112. The collection of abrasive particles of any one ofembodiments 90 and 111, wherein the Mean Non-Convexity Factor is atleast 3.75 or at least 4.0 or at least 4.5 or at least 5.0 or at least5.5 or at least 6.0 or at least 6.5 or at least 7.0 or at least 7.5 orat least 8.0 or at least 8.5 or at least 9.0.

Embodiment 113. The collection of abrasive particles of any one ofembodiments 90 and 111, wherein the Mean Non-Convexity Factor is notgreater than 30 or not greater than 25 or not greater than 20 or notgreater than 18 or not greater than 15 or not greater than 14 or notgreater than 13 or not greater than 12 or not greater than 11 or notgreater than 10.5.

Embodiment 114. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 91, and 92, further comprising a Non-ConvexityFactor Standard Deviation of at least 2.4.

Embodiment 115. The collection of abrasive particles of any one ofembodiments 90 and 114, wherein the Non-Convexity Factor StandardDeviation is at least 2.5 or at least 2.6 or at least 2.7 or at least2.8 or at least 2.9 or at least 3.0 or at least 3.1 or at least 3.2 orat least 3.3 or at least 3.4 or at least 3.5.

Embodiment 116. The collection of abrasive particles of any one ofembodiments 90 and 114, wherein the Non-Convexity Factor StandardDeviation is not greater than 30 or not greater than 25 or not greaterthan 20 or not greater than 15 or not greater than 10 or not greaterthan 8 or not greater than 6 or not greater than 4.

Embodiment 117. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, and 91, further comprising a standarddeviation of height of not greater than 100 microns and a MeanNon-Convexity Factor of at least 3.5.

Embodiment 118. The collection of abrasive particles of any one ofembodiments 91 and 117, wherein the standard deviation of height is notgreater than 90 microns or not greater than 85 microns or not greaterthan 80 microns or not greater than 75 microns or not greater than 70microns or not greater than 65 microns or not greater than 60 microns ornot greater than 55 microns or not greater than 50 microns or notgreater than 45 microns or not greater than 40 microns or not greaterthan 35 microns.

Embodiment 119. The collection of abrasive particles of any one ofembodiments 91 and 117, wherein the standard deviation of height is atleast 1 micron or at least 5 microns or at least 10 microns or at least15 microns or at least 20 microns or at least 25 microns or at least 30microns or at least 35 microns.

Embodiment 120. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, further comprising at least onefeature of the group consisting of:

a Mean Non-Convexity Factor of at least 3.5;a Non-Convexity Factor Standard Deviation of at least 2.4;a Mean Anisotropy Factor of at least 1.25;a standard deviation of height of not greater than 100 microns;or any combination thereof.

Embodiment 121. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, wherein the first major surfaceand second major surface are substantially parallel to each other.

Embodiment 122. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, further comprising a fixedabrasive including the collection of abrasive particles.

Embodiment 123. The collection of abrasive particles of embodiment 122,the fixed abrasive is a coated abrasive.

Embodiment 124. The collection of abrasive particles of embodiment 122,wherein the fixed abrasive is a bonded abrasive.

Embodiment 125. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, further comprising a first groupof abrasive particles, each of the abrasive particles in the first groupbeing a first abrasive particle.

Embodiment 126. The collection of abrasive particles of embodiment 125,further comprising a second group of abrasive particles, each of theabrasive particles in the second group being a second abrasive particle.

Embodiment 127. The collection of abrasive particles of embodiment 126,wherein the two-dimensional shape of the body of the first abrasiveparticle, as viewed in a plane defined by a length and a width of thebody, is selected from the first group consisting of regular polygons,irregular polygons, numerals, Greek alphabet characters, Latin alphabetcharacters, Russian alphabet characters, complex shapes having acombination of polygonal shapes, a shape with linear and curvedportions, and a combination thereof.

Embodiment 128. The collection of abrasive particles of embodiment 126,wherein the body of the first abrasive particle comprises atwo-dimensional shape as viewed in a plane defined by a length and awidth of the body that is an irregular polygonal shape.

Embodiment 129. The collection of abrasive particles of embodiment 126,wherein the two-dimensional shape of the body of the second abrasiveparticle, as viewed in a plane defined by a length and a width of thebody, is selected from the first group consisting of regular polygons,irregular polygons, numerals, Greek alphabet characters, Latin alphabetcharacters, Russian alphabet characters, complex shapes having acombination of polygonal shapes, a shape with linear and curvedportions, and a combination thereof.

Embodiment 130. The collection of abrasive particles of embodiment 126,wherein the body of the first abrasive particle comprises atwo-dimensional shape as viewed in a plane defined by a length and awidth of the body that is an irregular polygonal shape, and wherein thebody of the second abrasive particle comprises a two-dimensional shapeas viewed in a plane defined by a length and a width of the body that isan irregular polygonal shape different than the irregular polygonalshape of the body of the first abrasive particle.

Embodiment 131. The collection of abrasive particles of embodiment 126,wherein the body of the first abrasive particle includes a plurality ofside surface portions and a majority of the side surface portions aresubstantially planar.

Embodiment 132. The collection of abrasive particles of embodiment 131,wherein all of the side surface portions of the body of the firstabrasive particle are substantially planar.

Embodiment 133. The collection of abrasive particles of embodiment 131,wherein the first side surface portion has a curved contour.

Embodiment 134. The collection of abrasive particles of embodiment 131,wherein the first side surface portion has an irregular contour.

Embodiment 135. The collection of abrasive particles of embodiment 131,wherein the body of the first abrasive particle includes a plurality ofside surface portions, and each of the side surface portions extend fora length of at least 5% of a length of the body or at least 10% or atleast 15% or at least 20% or at least 25%.

Embodiment 136. The collection of abrasive particles of embodiment 131,wherein each of the side surface portions of the body of the firstabrasive particle extend for a length of not greater than 50% of alength of the body or not greater than 40% or not greater than 30%.

Embodiment 137. The collection of abrasive particles of embodiment 126,wherein further comprising a third abrasive particle comprising a bodyincluding a first major surface, a second major surface opposite thefirst major surface, and a side surface extending between the firstmajor surface and the second major surface, wherein the body of thesecond abrasive particle comprises a two-dimensional shape that isdifferent compared to the two-dimensional shape of the body of the firstabrasive particle and the two-dimensional shape of the body of thesecond abrasive particle.

Embodiment 138. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, wherein the body comprises afirst side surface portion extending for at least a portion of adistance between two external corners of the body and further comprisinga first protrusion extending for at least 30% of a total length of thefirst side surface portion of the side surface or at least 40% of thetotal length of the first side surface portion or at least 50% of thetotal length of the first side surface portion or at least 60% of thetotal length of the first side surface portion or at least 70% of thetotal length of the first side surface portion or at least 80% of thetotal length of the first side surface portion or at least 90% of thetotal length of the first side surface portion.

Embodiment 139. The collection of abrasive particles of embodiment 138,wherein the first side surface portion is defined as a portion of theside surface extending between two external corners of the body.

Embodiment 140. The collection of abrasive particles of embodiment 138,wherein the first side surface portion is a fraction of the total lengthof the side surface defining the perimeter of the body.

Embodiment 141. The collection of abrasive particles of embodiment 138,wherein the first protrusion extends for a fraction of the total lengthof the side surface defining the perimeter of the body.

Embodiment 142. The collection of abrasive particles of embodiment 138,wherein the first side surface portion and first protrusion havesubstantially the same contour as viewed in the plane of the first majorsurface.

Embodiment 143. The collection of abrasive particles of embodiment 138,wherein the first protrusion intersects a second side surface portionthat is distinct from the first side surface portion.

Embodiment 144. The collection of abrasive particles of embodiment 138,further comprising a first depression extending in a direction parallelto the first side surface portion of the side surface.

Embodiment 145. The collection of abrasive particles of embodiment 144,further comprising a second depression extending in a direction parallelto a second side surface portion, and further comprising a secondprotrusion disposed between the second side surface and the seconddepression, the second protrusion abutting the second side surfaceportion and extending along the second side surface portion.

Embodiment 146. The collection of abrasive particles of embodiment 138,wherein further comprising an unfeatured edge extending between thefirst major surface and a third side surface portion, wherein the thirdside surface portion is distinct from the first side surface portion.

Embodiment 147. The collection of abrasive particles of embodiment 146,wherein the third side surface portion and first side surface portionare separated from each other by at least one external corner on theside surface.

Embodiment 148. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, wherein the body includes abottom edge joining the second major surface and the side surface,wherein at least a portion of the bottom edge has an irregular contour.

Embodiment 149. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, wherein the body comprises atleast one material from the group of oxides, carbides, nitrides,borides, oxycarbides, oxynitrides, oxyborides, natural minerals,synthetic materials, carbon-based materials, and a combination thereof.

Embodiment 150. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, wherein further comprising:

a first group of abrasive particles, each of the abrasive particles inthe first group being a first abrasive particle; anda second group of abrasive particles, each of the abrasive particles inthe second group being a second abrasive particle; andwherein the body of the first abrasive particle includes at least onematerial from the group of oxides, carbides, nitrides, borides,oxycarbides, oxynitrides, oxyborides, natural minerals, syntheticmaterials, carbon-based materials, and a combination thereof.

Embodiment 151. The collection of abrasive particles of any one ofembodiments 149 and 150, wherein the body comprises alumina.

Embodiment 152. The collection of abrasive particles of embodiment 151,wherein the body consists essentially of alumina.

Embodiment 153. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, wherein the body includes atleast one oxide from the group of aluminum oxide, zirconium oxide,titanium oxide, yttrium oxide, chromium oxide, strontium oxide, siliconoxide, magnesium oxide, rare-earth oxides, or any combination thereof.

Embodiment 154. The collection of abrasive particles of embodiment 150,wherein the body of the second abrasive particle comprises a sidesurface portion that is substantially planar.

Embodiment 155. The collection of abrasive particles of embodiment 150,wherein the body of the second abrasive particle comprises a pluralityof side surface portions, and wherein a majority of the side surfaceportions are substantially planar.

Embodiment 156. The collection of abrasive particles of embodiment 155,wherein all of the side surface portions of the body of the secondabrasive particle are substantially planar.

Embodiment 157. The collection of abrasive particles of embodiment 155,wherein the body of the second abrasive particle comprises a sidesurface portion that has a curved contour.

Embodiment 158. The collection of abrasive particles of embodiment 155,wherein the body of the second abrasive particle comprises a sidesurface portion that has an irregular contour.

Embodiment 159. The collection of abrasive particles of embodiment 150,wherein the body of the first abrasive particle includes a plurality ofside surface portions, and each of the side surface portions extend fora length of at least 5% of a length of the body or at least 10% or atleast 15% or at least 20% or at least 25%.

Embodiment 160. The collection of abrasive particles of embodiment 159,wherein each of the side surface portions of the body of the firstabrasive particle extend for a length of not greater than 80% of alength of the body or not greater than 70% or not greater than 60% ornot greater than 50% or not greater than 40% or not greater than 30%.

Embodiment 161. The collection of abrasive particles of embodiment 150,wherein the first major surface of the body of the second abrasiveparticle comprises a first protrusion abutting the first side surfaceportion and extending along the first side surface portion.

Embodiment 162. The collection of abrasive particles of embodiment 161,wherein the first major surface of the body of the second abrasiveparticle comprises a first depression extending in a direction parallelto a first side surface portion.

Embodiment 163. The collection of abrasive particles of embodiment 161,wherein the first protrusion extends for at least 30% of a total lengthof the first side surface portion or at least 40% of the total length ofthe first side surface portion or at least 50% of the total length ofthe first side surface portion or at least 60% of the total length ofthe first side surface portion or at least 70% of the total length ofthe first side surface portion or at least 80% of the total length ofthe first side surface portion or at least 90% of the total length ofthe first side surface portion.

Embodiment 164. The collection of abrasive particles of embodiment 161,wherein the first side surface portion is defined as a portion of theside surface extending between two external corners of the body.

Embodiment 165. The collection of abrasive particles of embodiment 161,wherein the first side surface portion is a fraction of the total lengthof the side surface defining the perimeter of the body.

Embodiment 166. The collection of abrasive particles of embodiment 161,wherein the first protrusion extends for a fraction of the total lengthof the side surface defining the perimeter of the body.

Embodiment 167. The collection of abrasive particles of embodiment 161,the first side surface portion and the first protrusion havesubstantially the same contour as viewed in the plane of the first majorsurface.

Embodiment 168. The collection of abrasive particles of embodiment 161,wherein the first protrusion intersects a second side surface portionthat is distinct from the first side surface portion.

Embodiment 169. The collection of abrasive particles of any one ofembodiments 87, 89, 90, 91, and 92, wherein a majority of the abrasiveparticles of the collection of abrasive particles comprise a pluralityof microridges along at least a portion of the side surface of the body.

Embodiment 170. The collection of abrasive particles of any one ofembodiments 88 and 169, wherein at least 51% of the abrasive particlesof the collection of abrasive particles include the plurality ofmicroridges or at least 52% or at least 54% or at least 56% or at least58% or at least 60% or at least 62% or at least 64% or at least 66% orat least 68% or at least 70% or at least 72% or at least 74% or at least76% or at least 78% or at least 80% or at least 82% or at least 84% orat least 86% or at least 88% or at least 90% or at least 92% or at least94% or at least 96% or at least 98% or at least 99% of the abrasiveparticles of the collection of abrasive particles.

Embodiment 171. The collection of abrasive particles of any one ofembodiments 88 and 169, wherein not greater than 99% of the abrasiveparticles of the collection of abrasive particles include the pluralityof microridges or not greater than 98% or not greater than 96% or notgreater than 94% or not greater than 92% or not greater than 90% or notgreater than 88% or not greater than 86% or not greater than 84% or notgreater than 82% or not greater than 80% or not greater than 78% or notgreater than 76% or not greater than 74% or not greater than 72% or notgreater than 70% or not greater than 68% or not greater than 66% or notgreater than 64% or not greater than 62% or not greater than 60% or notgreater than 58% or not greater than 56% or not greater than 54% or notgreater than 52% of the abrasive particles of the collection of abrasiveparticles.

Embodiment 172. The collection of abrasive particles of any one ofembodiments 88 and 169, wherein a majority of the total surface area ofthe side surfaces of the abrasive particles in the collection ofabrasive particles comprise a plurality of microridges.

Embodiment 173. The collection of abrasive particles of embodiment 172,wherein at least 51% of the total surface area of the side surfaces ofthe abrasive particles of the collection includes the plurality ofmicroridges or at least 52% or at least 54% or at least 56% or at least58% or at least 60% or at least 62% or at least 64% or at least 66% orat least 68% or at least 70% or at least 72% or at least 74% or at least76% or at least 78% or at least 80% or at least 82% or at least 84% orat least 86% or at least 88% or at least 90% or at least 92% or at least94% or at least 96% or at least 98% or at least 99%.

Embodiment 174. The collection of abrasive particles of embodiment 172,wherein not greater than 99% of the total surface area of the sidessurfaces of the abrasive particles of the collection includes theplurality of microridges or not greater than 98% or not greater than 96%or not greater than 94% or not greater than 92% or not greater than 90%or not greater than 88% or not greater than 86% or not greater than 84%or not greater than 82% or not greater than 80% or not greater than 78%or not greater than 76% or not greater than 74% or not greater than 72%or not greater than 70% or not greater than 68% or not greater than 66%or not greater than 64% or not greater than 62% or not greater than 60%or not greater than 58% or not greater than 56% or not greater than 54%or not greater than 52%.

Embodiment 175. The collection of abrasive particles of any one ofembodiments 88 and 169, wherein at least a portion of the plurality ofmicroridges comprises a plurality of isolated microridges defined bymicroridges extending from the side surface and separated by generallysmooth planar regions.

Embodiment 176. The collection of abrasive particles of embodiment 175,wherein the plurality of isolated microridges extend along the sidesurface in an irregular path.

Embodiment 177. The collection of abrasive particles of embodiment 175,wherein at least one of the isolated microridges of the plurality ofisolated microridges comprises a head region and a tail region connectedto and extending from the head region, wherein the head region has arounded shape and the tail region has an elongated shape.

Embodiment 178. The collection of abrasive particles of any one ofembodiments 88 and 169, wherein at least a portion of the plurality ofmicroridges comprises a plurality of scaled microridges.

Embodiment 179. The collection of abrasive particles of embodiment 178,wherein at least a portion of the scaled microridges of the plurality ofscaled microridges comprise a primary ridge and a plurality of wrinklesextending from the primary ridge.

Embodiment 180. The collection of abrasive particles of embodiment 179,wherein the primary ridge extends along the side surface in an irregularpath.

Embodiment 181. The collection of abrasive particles of embodiment 179,wherein at least a portion of the plurality of wrinkles extend along theside surface in an irregular path away from the primary ridge.

Embodiment 182. The collection of abrasive particles of embodiment 179,wherein the wrinkles define grooves extending along the side surfacealong an irregular path.

Embodiment 183. The collection of abrasive particles of embodiment 179,wherein the wrinkles extend along a curved path.

Embodiment 184. The collection of abrasive particles of embodiment 179,wherein the plurality of scaled microridges includes a greater number ofwrinkles compared to the number of primary ridges.

Embodiment 185. The collection of abrasive particles of embodiment 179,wherein the wrinkles extend in a different direction compared to one ormore primary ridges, and the wrinkles extend between two or more primaryridges.

Embodiment 186. The collection of abrasive particles of embodiment 179,wherein the primary ridge includes at least one gap between elongatedportions.

Embodiment 187. The collection of abrasive particles of embodiment 178,wherein at least a portion of the scaled microridges have a scaledappearance.

Embodiment 188. The collection of abrasive particles of embodiment 178,wherein at least a portion of the scaled microridges have a layeredappearance.

Embodiment 189. The collection of abrasive particles of embodiment 178,wherein at least a portion of the scaled microridges include a pluralityof raised portions with irregular shapes and wrinkles extending betweenthe plurality of raised portions.

Embodiment 190. The collection of abrasive particles of any one ofembodiments 88 and 169, wherein the plurality of microridges is aconchoidal fracturing feature.

Embodiment 191. The collection of abrasive particles of any one ofembodiments 88 and 169, wherein the plurality of microridges is formedduring fracturing of the side surface.

Embodiment 192. The collection of abrasive particles of any one ofembodiments 88 and 169, wherein the plurality of microridges includes aprecipice region.

Embodiment 193. The collection of abrasive particles of any one ofembodiments 87, 88, 89, 90, 91, and 92, wherein the side surface of thebody includes side surface portions, and wherein each side surfaceportion extends between external corners of the body, and wherein atleast 45% of the side surface portions include the plurality ofmicroridges.

Embodiment 194. The collection of abrasive particles of embodiment 193,wherein the body includes at least three side surface portions includingthe plurality of microridges.

Embodiment 195. The collection of abrasive particles of embodiment 193,wherein all of the side surface portions include the plurality ofmicroridges.

Embodiment 196. The collection of abrasive particles of embodiment 193,wherein, wherein at least 52% of the side surface portions of the bodyinclude the plurality of microridges, or at least 54% or at least 56% orat least 58% or at least 60% or at least 62% or at least 64% or at least66% or at least 68% or at least 70% or at least 72% or at least 74% orat least 76% or at least 78% or at least 80% or at least 82% or at least84% or at least 86% or at least 88% or at least 90% or at least 92% orat least 94% or at least 96% or at least 98% or at least 99%.

Embodiment 197. The collection of abrasive particles of embodiment 193,wherein the body includes at least one side surface portion that doesnot include the plurality of microridges.

Embodiment 198. The collection of abrasive particles of embodiment 193,wherein at least 10% of the abrasive particles of the collection have atleast 45% of the side surface portions including the plurality ofmicroridges.

Embodiment 199. The collection of abrasive particles of embodiment 193,wherein each of the abrasive particles of the collection has at least45% of the side surface portions including the plurality of microridges.

EXAMPLES

A variety of abrasive particles were made according to the followingconditions.

A first sample, Sample S1, was initially formed from a mixture includingapproximately 37-43 wt % boehmite, water and nitric acid. One may use acommercially available boehmite, such as Disperal from Sasol Corp. Thenitric acid-to-boehmite ratio was approximately 0.035. The boehmite wasmixed and seeded with 1% alpha alumina seeds relative to the totalalumina content of the mixture. The alpha alumina seeds were made bymilling of corundum using conventional techniques, described for examplein U.S. Pat. No. 4,623,364. The ingredients were mixed in a planetarymixer of conventional design and mixed under reduced pressure to removegaseous elements from the mixture (e.g., bubbles).

The mixture was then cast onto a belt using an extruder. The mixtureformed a layer having a width of approximately 8 cm and a height ofapproximately 0.4 mm. The surface of the belt in contact with themixture was Invar 36. The extrusion and formation of the mixture into alayer was conducted under standard ambient conditions of temperature,pressure, and atmosphere.

After forming the mixture, various modifications were conducted tocreate different samples of abrasive particles. In particular, the layerwas shaped with various different forms having different features.

Example 1

The mixture was formed into a layer as described above and the uppersurface of the layer was modified using a form having square-shapedopenings, such as the form illustrated in FIGS. 3A and 3B. Eachsquare-shaped opening had four sides defining the openings, and eachside was approximately 1.7 mm in length. The form was made of siliconeand was pressed (by hand) into the upper surface of the body on thebelt. Sufficient force was applied to create lines in the upper surfaceof the body corresponding to the arrangement of features on the form.

The modified body was conveyed to a drying zone including two 4000W IRlamps mounted in parallel, side-by-side over the upper surface of themodified body. Each lamp was 40 inches long, 2.5 inch wide, and was usedat 35% of the maximum power (i.e., 1400W). The drying temperature withinthe drying zone was set for 70° C., which was controlled by athermocouple placed approximately 1 cm above the upper surface of themodified body. Air having a relative humidity of approximately 50%(+15%) was flowed into the drying zone at a flow rate of approximately1.5 m/s. The drying zone was partially enclosed, having openings atopposite ends to allow air to flow through the enclosure. The enclosurewas 2 meters in length, 0.5 meters in height, and 0.5 meters wide.

Drying was conducted under the conditions noted above to achievecontrolled cracking of the body and formation of precursor abrasiveparticles. That is, after modifying the body with the form, the dryingconditions were sufficient to crack the modified body in a manner tocreate a plurality of precursor abrasive particles from the body. Thenature of the pattern in the body that was created by the forminfluenced the cracking behavior during the drying process to facilitatethe formation of the precursor abrasive particles.

The dried abrasive particles were then sintered at a sinteringtemperature of approximately 1400° C. for 10 minutes in a rotary tubefurnace of standard atmospheric pressure and an atmosphere of air.

FIGS. 13A-13R provide top-down images of the particles producedaccording to the method of Example 1. The images from FIGS. 13A-13Rinclude images taken with a Nanovea microscope wherein the colordifferences represent differences in height along the particle surfaces.Notably, some of the particles did not section along the features formedduring the process of modifying the body and evidence of the featuresexists within these abrasive particles (e.g., FIGS. 13A-13F). Otherparticles appear to have cracked along the features formed during themodification process (e.g., FIGS. 13G-13L) and such abrasive particleshave two-dimensional shapes substantially corresponding to the shape ofthe openings in the form used to pattern the body. Such abrasiveparticles also have a size that generally corresponds to the size of theopenings in the form used to pattern the body (provided some shrinkageoccurred during calcination and sintering). Other abrasive particles(e.g., FIGS. 13M-13R) include images of abrasive particles formedaccording to Example 1, where the particles appear to have cracked nearthe features formed in the body, but some evidence of the features(e.g., protrusions or grooves) exist within the abrasive particles. Suchfeatures are typically located near the side walls of the abrasiveparticles. Moreover, those features depicted and described in FIGS. 15A,15B, 16 and 17 are representative of the abrasive particles made fromExample 1.

Example 2

Abrasive particles were formed using the process of creating the mixtureas noted above and using the conditions provided in Example 1, exceptthat the body was modified using a form as depicted in FIGS. 4C and 4D.The form was a 3D printed object. The form was pressed (by hand) againstthe mixture on the belt with sufficient force to create a pattern offeatures (e.g., depressions) in the upper surface of the bodycorresponding to the pattern of features in the form. FIGS. 12A-12Jinclude images of the abrasive particles formed according to Example 2.

Example 3

Abrasive particles were formed using the process of creating the mixtureas noted above and using the conditions outlined in Example 1, exceptthat the body was modified using a form as depicted in FIGS. 4G and 4H.The form was a 3D printed object. The form was pressed (by hand) againstthe mixture on the belt with sufficient force to create a pattern offeatures (e.g., depressions) in the upper surface of the bodycorresponding to the pattern of features in the form. FIGS. 14A-14Jinclude images of the abrasive particles formed according to Example 3.

Example 4

Abrasive particles were formed using the process of Example 1, with theexception that the mixture was patterned from a form made of PEEK andthe form was pressed against the surface of the mixture via amotor-driven roller. These abrasive particles of this sample formed acollection and are referred to herein as Sample S4. A representativeimage of an abrasive particle from the collection is provided in FIGS.18-20. The collection of abrasive particles had a MAF of approximately3.80, an Anisotropy Factor Standard Deviation of approximately 1.14, aMAF difference between the first region and second region of greaterthan 3, a Mean Non-Convexity Factor of 9.28, a Non-Convexity FactorStandard Deviation of 3.54, an average height of the body of 228microns, a standard deviation of height of approximately 46 microns, afirst region average height of 68 microns, a second region averageheight of 172 microns.

An analysis was completed on other types of conventional abrasiveparticles to evaluate the differences between such particles and therepresentative particles of Sample S4. A first conventional collectionof particles, Sample CS1, was obtained and is representative of atriangular shaped abrasive particle available from 3M as Cubitron II.FIG. 23A includes a top-down image of an abrasive particle from SampleCS1. FIG. 23B includes an image of a portion of a side surface of anabrasive particle from Sample CS1.

A second collection of conventional particles, Sample CS2, was obtainedand is representative of conventional crushed abrasive particles. FIG.24A includes a top-down image of a particle of Sample CS2. FIG. 24Bincludes an image of a portion of a side surface of an abrasive particleof Sample CS2. Such particles are commercially available as Cerpass 24Grit from Saint-Gobain Corporation.

Finally, a third collection of conventional abrasive particles, SampleCS3, was obtained and is representative of particles that were castedinto a layer of material that was later cut by blades. FIG. 25A includesa top-down image of a particle of Sample CS3. FIG. 25B includes an imageof a portion of a side surface of an abrasive particle of Sample CS2.

The abrasive particles of Sample CS1 had a MAF of approximately 0.64, anAnisotropy Factor Standard Deviation of approximately 0.49, a MeanNon-Convexity Factor of 3.32, a Non-Convexity Factor Standard Deviationof 0.73, and an average height of the body of 290 microns.

As the abrasive particles of Sample CS1 are shaped abrasive particlespresumably made through a molding process, the sidewalls of theparticles did not exhibit noticeably different regions, such as a firstregion and second region as was demonstrated by the representativeabrasive particles of Sample S4.

The collection of abrasive particles of Sample CS2 had a MAF ofapproximately 1.21, an Anisotropy Factor Standard Deviation ofapproximately 0.72, a Mean Non-Convexity Factor of 12.9, a Non-ConvexityFactor Standard Deviation of 3.65, an average height of the body of 514microns, a standard deviation of height of approximately 106 microns. Asthe abrasive particles of Sample CS2 are crushed abrasive particles, thesidewalls of the particles did not exhibit noticeably different regions,such as a first region and second region as was demonstrated by therepresentative abrasive particles of Sample S4.

The collection of abrasive particles of Sample CS3 had a MeanNon-Convexity Factor of 9.40, a Non-Convexity Factor Standard Deviationof 2.33. The MAF was not measured, but given what is provided in theimages, the majority of the sidewall regions would likely have a MAFless than the representative abrasive particles of Sample S4. The sameis expected of the Anisotropy Factor Standard Deviation. As illustratedin FIG. 25B the abrasive particles of Sample CS3 generally had sidewallsthat included first and second regions 2502 and 2503, respectively. Theaverage height of the body was approximately 289 microns and thestandard deviation of the height was approximately 57 microns. Thesecond region 2503 was notably smaller in height compared to the firstregion 2502. The second region 2503 had an average height of 18 micronsand the first region 2502 had an average height of approximately 271microns. The height of the second region 2503 relative to the height ofthe body 2501 was approximately 6%. The first region 2502 has a notablysmoother and less textured surface compared to the second region 2503.

The present application represents a departure from the state of theart. While the industry has recognized that abrasive particles may beformed through processes such as molding and screen printing, theprocesses of the embodiments herein are distinct from such processes.Notably, the embodiments herein utilize a combination of processfeatures that facilitate the formation of abrasive particles having oneor a combination of unique features. Such features can include, but arenot limited to, shape, size, features in one or more major surfaces,composition, and others as described in the embodiments herein.Moreover, the processes of the embodiments herein facilitate theformation of a shaped abrasive particle or a batch of abrasiveparticles, having one or more characteristics, including one or morecombination of the features of the abrasive particles. Certain abrasiveparticles and batches containing abrasive particles of the embodimentsherein may have features that enable enhanced performance in the contextof fixed abrasive articles.

The above-disclosed subject matter is to be considered illustrative, andnot restrictive, and the appended claims are intended to cover all suchmodifications, enhancements, and other embodiments, which fall withinthe true scope of the present invention. Thus, to the maximum extentallowed by law, the scope of the present invention is to be determinedby the broadest permissible interpretation of the following claims andtheir equivalents, and shall not be restricted or limited by theforegoing detailed description.

The Abstract of the Disclosure is provided to comply with Patent Law andis submitted with the understanding that it will not be used tointerpret or limit the scope or meaning of the claims. In addition, inthe foregoing Detailed Description, various features may be groupedtogether or described in a single embodiment for the purpose ofstreamlining the disclosure. This disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter may be directed toless than all features of any of the disclosed embodiments. Thus, thefollowing claims are incorporated into the Detailed Description, witheach claim standing on its own as defining separately claimed subjectmatter.

1. A collection of abrasive particles, wherein each abrasive particle ofthe collection of abrasive particles comprises: a body having a firstmajor surface, a second major surface opposite the first major surface,and a side surface extending between the first major surface and thesecond major surface, wherein the side surface comprises a MeanAnisotropy Factor of at least 1.25.
 2. The collection of abrasiveparticles of claim 1, wherein the collection of abrasive particlescomprises a Mean Non-Convexity Factor of at least 3.5.
 3. The collectionof abrasive particles of claim 1, wherein the body comprises a height asdefined as the distance along the side surface between the first majorsurface and the second major surface and wherein the collection ofabrasive particles comprises a standard deviation of height of notgreater than
 100. 4. The collection of abrasive particles of claim 1,further comprising an Anisotropy Factor Standard Deviation of at least0.75 and not greater than
 10. 5. The collection of abrasive particles ofclaim 1, wherein the side surface comprises a first region extendingfrom the first major surface and a second region extending from thesecond major surface, and wherein the first region and second regionabut on the side surface, and wherein the second region extends for agreater percentage of the height as compared to the first region.
 6. Thecollection of abrasive particles of claim 5, wherein the second regionextends for a greater percentage of the height as compared to the firstregion.
 7. The collection of abrasive particles of claim 5, wherein thefirst region has an average height of not greater than 90% of the heightof the body.
 8. The collection of abrasive particles of claim 5, whereinthe second region comprises an average height of not greater than 90% ofthe height of the body or not greater than 80% or not greater than 70%or not greater than 60% or not greater than 50% or not greater than 40%or not greater than 30% or not greater than 20% or not greater than 10%or not greater than 5%.
 9. The collection of abrasive particles of claim5, wherein the first region comprises a Mean Anisotropy Factor of notgreater than 1.20.
 10. The collection of abrasive particles of claim 5,wherein the Mean Anisotropy Factor of the second region is at least1.30.
 11. The collection of abrasive particles of claim 5, wherein theMean Anisotropy Factor of the second region is not greater than 20 ornot greater than 15 or not greater than 12 or not greater than 10 or notgreater than 8 or not greater than 7 or not greater than 6 or notgreater than 5 or not greater than
 4. 12. The collection of abrasiveparticles of claim 5, wherein the second region comprises a plurality ofmicroridges.
 13. The collection of abrasive particles of claim 12,wherein the plurality of microridges is a conchoidal fracturing feature.14. The collection of abrasive particles of claim 12, wherein theplurality of microridges is formed during controlled cracking of theside surface.
 15. The collection of abrasive particles of claim 12,wherein at least 51% of the total surface area of the side surfaceincludes the plurality of microridges.
 16. The collection of abrasiveparticles of claim 2, further comprising a Non-Convexity Factor StandardDeviation of at least 2.4.
 17. The collection of abrasive particles ofclaim 1, wherein the Mean Anisotropy Factor is at least 1.30 and notgreater than
 20. 18. The collection of abrasive particles of claim 1,wherein the Mean Anisotropy Factor is at least 2.0.
 19. The collectionof abrasive particles of claim 1, wherein the Mean Anisotropy Factor isat least 3.0.
 19. (canceled)
 20. The collection of abrasive particles ofclaim 1, further comprising a fixed abrasive including the collection ofabrasive particles, and wherein the fixed abrasive is a coated abrasiveor a bonded abrasive.